## Numerical

The refractive index of a transparent liquid filled in an equilateral hollow prism is $\sqrt{2}$. The angle of minimum deviation for the liquid will b...

A bi convex lens of focal length $$10 \mathrm{~cm}$$ is cut in two identical parts along a plane perpendicular to the principal axis. The power of eac...

A fish rising vertically upward with a uniform velocity of $$8 \mathrm{~ms}^{-1}$$, observes that a bird is diving vertically downward towards the fis...

Two convex lenses of focal length $$20 \mathrm{~cm}$$ each are placed coaxially with a separation of $$60 \mathrm{~cm}$$ between them. The image of th...

As shown in the figure, a plane mirror is fixed at a height of $$50 \mathrm{~cm}$$ from the bottom of tank containing water $$\left(\mu=\frac{4}{3}\ri...

The radius of curvature of each surface of a convex lens having refractive index 1.8 is $$20 \mathrm{~cm}$$. The lens is now immersed in a liquid of r...

A point object, 'O' is placed in front of two thin symmetrical coaxial convex lenses $$\mathrm{L}_{1}$$ and $$\mathrm{L}_{2}$$ with focal length $$24 ...

Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature $$30 \mathrm{~cm}$$...

Two vertical parallel mirrors A and B are separated by $$10 \mathrm{~cm}$$. A point object $$\mathrm{O}$$ is placed at a distance of $$2 \mathrm{~cm}$...

A pole is vertically submerged in swimming pool, such that it gives a length of shadow $$2.15 \mathrm{~m}$$ within water when sunlight is incident at ...

A thin cylindrical rod of length $$10 \mathrm{~cm}$$ is placed horizontally on the principle axis of a concave mirror of focal length $$20 \mathrm{~cm...

In an experiment for estimating the value of focal length of converging mirror, image of an object placed at $$40 \mathrm{~cm}$$ from the pole of the ...

In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of th...

An object is placed on the principal axis of convex lens of focal length 10cm as shown. A plane mirror is placed on the other side of lens at a distan...

A ray of light is incident from air on a glass plate having thickness $$\sqrt3$$ cm and refractive index $$\sqrt2$$. The angle of incidence of a ray i...

A convex lens of refractive index 1.5 and focal length 18cm in air is immersed in water. The change in focal length of the lens will be ___________ cm...

As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The rad...

The X-Y plane be taken as the boundary between two transparent media $$\mathrm{M}_{1}$$ and $$\mathrm{M}_{2}$$. $$\mathrm{M}_{1}$$ in $$Z \geqslant 0$...

An object 'O' is placed at a distance of $$100 \mathrm{~cm}$$ in front of a concave mirror of radius of curvature $$200 \mathrm{~cm}$$ as shown in the...

In an experiment with a convex lens, The plot of the image distance $$\left(v^{\prime}\right)$$ against the object distance ($$\left.\mu^{\prime}\righ...

A thin prism of angle $$6^{\circ}$$ and refractive index for yellow light $$\left(\mathrm{n}_{\mathrm{Y}}\right) 1.5$$ is combined with another prism ...

In the given figure, the face $$A C$$ of the equilateral prism is immersed in a liquid of refractive index '$$n$$'. For incident angle $$60^{\circ}$$ ...

The graph between $$\frac{1}{u}$$ and $$\frac{1}{v}$$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure....

A convex lens of focal length 20 cm is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and...

The refractive index of an equilateral prism is $$\sqrt 2 $$. The angle of emergence under minimum deviation position of prism, in degree, is ________...

A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive index 1.5. The distance from the centre ...

A small bulb is placed at the bottom of a tank containing water to a depth of $$\sqrt7$$ m. The refractive index of water is $${4 \over 3}$$. The area...

A light ray is incident, at an incident angle $$\theta$$1, on the system of tow plane mirrors M1 and M2 having an inclination angle 75$$^\circ$$ betwe...

A ray of light is incident at an angle of incidence 60$$^\circ$$ on the glass slab of refractive index $$\sqrt3$$. After refraction, the light ray eme...

Two identical thin biconvex lens of focal length 15 cm and refractive index 1.5 are in contact with each other. The space between the lenses is filled...

Cross-section view of a prism is the equilateral triangle ABC in the figure. The minimum deviation is observed using this prism when the angle of inci...

An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on other side of lens at 8 cm as shown ...

A prism of refractive index n1 and another prism of refractive index n2 are stuck together (as shown in the figure). n1 and n2 depend on $$\lambda$$, ...

A ray of light passing through a prism ($$\mu$$ = $$\sqrt 3 $$) suffers minimum deviation. It is found that the angle of incidence is double the angle...

An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification '6', gives an unresolved image. A resolved image is ...

The image of an object placed in air formed by a convex refracting surface is at a distance of 10 m behind the surface. The image is real and is at $$...

A deviation of 2$$^\circ$$ is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of ...

A point source of light S, placed at a distance 60cm in front of the centre of a plane mirror of width 50 cm, hangs vertically on a wall. A man walks...

The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of convex lens is ____...

A prism of angle A = 1o has a refractive index
$$\mu $$ = 1.5. A good estimate for the minimum angle
of deviation (in degrees) is close to $${N \over ...

A compound microscope consists of an
objective lens of focal length 1 cm and an
eyepiece of focal length 5 cm with a separation
of 10 cm.
The distance...

The distance between an object and a screen is 100 cm. A lens can produce real image of the
object on the screen for two different positions between t...

In a compound microscope, the magnified virtual image is formed at a distance of 25 cm from the
eye-piece. The focal length of its objective lens is 1...

When an object is kept at a distance of 30 cm from a concave mirror, the image is formed at a
distance of 10 cm from the mirror. If the object is move...

An observer can see through a small hole on the side of a jar (radius 15 cm) at a point at height of
15 cm from the bottom (see figure). The hole is a...

A light ray enters a solid glass sphere of
refractive index $$\mu $$ = $$\sqrt 3 $$ at an angle of incidence
60o. The ray is both reflected and refrac...

A point object in air is in front of the curved
surface of a plano-convex lens. The radius of
curvature of the curved surface is 30 cm and
the refract...

## MCQ (Single Correct Answer)

A vessel of depth '$$d$$' is half filled with oil of refractive index $$n_{1}$$ and the other half is filled with water of refractive index $$n_{2}$$....

An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is $$12 \mathrm{~cm}$$. When viewed from the opposite s...

When one light ray is reflected from a plane mirror with $$30^{\circ}$$ angle of reflection, the angle of deviation of the ray after reflection is :...

The critical angle for a denser-rarer interface is $$45^{\circ}$$. The speed of light in rarer medium is $$3 \times 10^{8} \mathrm{~m} / \mathrm{s}$$....

An object is placed at a distance of 12 cm in front of a plane mirror. The virtual and erect image is formed by the mirror. Now the mirror is moved by...

In a reflecting telescope, a secondary mirror is used to:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The phase difference of two light wa...

A 2 meter long scale with least count of $$0.2 \mathrm{~cm}$$ is used to measure the locations of objects on an optical bench. While measuring the foc...

A monochromatic light wave with wavelength $$\lambda_{1}$$ and frequency $$v_{1}$$ in air enters another medium. If the angle of incidence and angle o...

Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between im...

A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index $\frac{5}{3}$
is poured inside the bucket, then the m...

A thin prism $P_1$ with an angle $6^{\circ}$ and made of glass of refractive index $1.54$ is combined with another prism $P_2$ made from glass of refr...

A person has been using spectacles of power $$-1.0$$ dioptre for distant vision and a separate reading glass of power $$2.0$$ dioptres. What is the le...

A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should. (Select the best ...

The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are :-
A. Real
B...

When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different poi...

Light enters from air into a given medium at an angle of $$45^{\circ}$$ with interface of the air-medium surface. After refraction, the light ray is d...

The power of a lens (biconvex) is $$1.25 \mathrm{~m}^{-1}$$ in particular medium. Refractive index of the lens is 1.5 and radii of curvature are $$20 ...

As shown in the figure, after passing through the medium 1 . The speed of light $$v_{2}$$ in medium 2 will be :
$$\left(\right.$$ Given $$\mathrm{c}=3...

In normal adujstment, for a refracting telescope, the distance between objective and eye piece is $$30 \mathrm{~cm}$$. The focal length of the objecti...

A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a light whose wavelength in air is...

Light travels in two media $$M_{1}$$ and $$M_{2}$$ with speeds $$1.5 \times 10^{8} \mathrm{~ms}^{-1}$$ and $$2.0 \times 10^{8} \mathrm{~ms}^{-1}$$ res...

For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm from the lens. A glass ...

Which of the following statement is correct?

Time taken by light to travel in two different materials $$A$$ and $$B$$ of refractive indices $$\mu_{A}$$ and $$\mu_{B}$$ of same thickness is $$t_{1...

Find the ratio of maximum intensity to the minimum intensity in the interference pattern if the widths of the two slits in Young's experiment are in t...

The speed of light in media 'A' and 'B' are $$2.0 \times {10^{10}}$$ cm/s and $$1.5 \times {10^{10}}$$ cm/s respectively. A ray of light enters from t...

The refracting angle of a prism is A and refractive index of the material of the prism is cot (A/2). Then the angle of minimum deviation will be -...

The aperture of the objective is 24.4 cm. The resolving power of this telescope, if a light of wavelength 2440 $$\mathop A\limits^o $$ is used to see ...

A convex lens has power P. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpen...

Consider a light ray travelling in air is incident into a medium of refractive index $$\sqrt{2n}$$. The incident angle is twice that of refracting ang...

A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air. The angle of...

The difference of speed of light in the two media A and B (vA $$-$$ vB) is 2.6 $$\times$$ 107 m/s. If the refractive index of medium B is 1.47, then t...

Two light beams of intensities in the ratio of 9 : 4 are allowed to interfere. The ratio of the intensity of maxima and minima will be :

A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water ($$\mu$$ = 4/3) into it while looking at the surface ...

An object is placed at the focus of concave lens having focal length f. What is the magnification and distance of the image from the optical centre of...

Two plane mirrors M1 and M2 are at right angle to each other shown. A point source 'P' is placed at 'a' and '2a' meter away from M1 and M2 respectivel...

Curved surfaces of a plano-convex lens of refractive index $$\mu$$1 and a plano-concave lens of refractive index $$\mu$$2 have equal radius of curvatu...

An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is d1 from C and the distance of the i...

Find the distance of the image from object O, formed by the combination of lenses in the figure :...

Car B overtakes another car A at a relative speed of 40 ms$$-$$1. How fast will the image of car B appear to move in the mirror of focal length 10 cm ...

The expected graphical representation of the variation of angle of deviation '$$\delta$$' with angle of incidence 'i' in a prism is :

A prism of refractive index $$\mu$$ and angle of prism A is placed in the position of minimum angle of deviation. If minimum angle of deviation is als...

A ray of light entering from air into a denser medium of refractive index $${4 \over 3}$$, as shown in figure. The light ray suffers total internal re...

A ray of laser of a wavelength 630 nm is incident at an angle of 30$$^\circ$$ at the diamond-air interface. It is going from diamond to air. The refra...

A ray of light passes from a denser medium to a rarer medium at an angle of incidence i. The reflected and refracted rays make an angle of 90$$^\circ$...

Region I and II are separated by a spherical surface of radius 25 cm. An object is kept in region I at a distance of 40 cm from the surface. The dista...

Three rays of light, namely red (R), green (G) and blue (B) are incident on the face PQ of a right angled prism PQR as shown in the figure.The refract...

Your friend is having eye sight problem. She is not able to see clearly a distant uniform window mesh and it appears to her as non-uniform and distort...

The thickness at the centre of a plane convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is 2 $$\times$$...

The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is placed in a medium of same refractive index? Ass...

Red light differs from blue light as they have :

The angle of deviation through a prism is minimum when(A) Incident ray and emergent ray are symmetric to the prism.(B) The refracted ray inside the pr...

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $$\overrightarrow a $$, $$\overrightarrow b $$ and $$\ove...

Given below are two statements : one is labeled as Assertion A and the other is labeled as Reason R.Assertion A : For a simple microscope, the angular...

A short straight object of height 100 cm lies before the central axis of a spherical mirror whose focal length has absolute value | f | = 40 cm. The i...

The focal length f is related to the radius of curvature r of the spherical convex mirror by :

A double convex lens has power P and same radii of curvature R of both the surfaces. The radius of
curvature of a surface of a plano-convex lens made ...

A point like object is placed at a distance of 1 m in front of a convex lens of focal length 0.5 m. A
plane mirror is placed at a distance of 2 m behi...

For a concave lens of focal length f, the relation
between object and image distances u and v,
respectively, from its pole can best be
represented by ...

A spherical mirror is obtained as shown in the
figure from a hollow glass sphere. If an object
is positioned in front of the mirror, what will be
the...

There is a small source of light at some depth
below the surface of water (refractive
index = $${4 \over 3}$$) in a tank of large cross sectional
surf...

A vessel of depth 2h is half filled with a liquid
of refractive index $$2\sqrt 2 $$ and the upper half with
another liquid of refractive index $$\sqrt...

An object is gradually moving away from the
focal point of a concave mirror along the axis
of the mirror. The graphical representation of
the magnitud...

The magnifying power of a telescope with tube
60 cm is 5. What is the focal length of its eye
piece ?

The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability $${4 \over 3}$$ for this...

A thin lens made of glass (refractive index = 1.5) of focal length f = 16 cm is immersed in a liquid
of refractive index 1.42. If its focal length in ...

If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5 mm, the focal length of the eye-...

A transparent cube of side, made of a material of refractive index $$\mu $$2, is immersed in a liquid of refractive
index $$\mu $$1($$\mu $$1 < $$\...

A concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5
cm (see figure). If a small particle i...

The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal length of the lens used?
...

One plano-convex and one plano-concave lens
of same radius of curvature 'R' but of different
materials are joined side by side as shown in
the figure....

A ray of light AO in vacuum is incident on a
glass slab at angle 60° and refracted at angle 30°
along OB as shown in the figure. The optical path
leng...

A thin convex lens L (refractive index = 1.5)
is placed on a plane mirror M. When a pin is
placed at A, such that OA = 18 cm, its real
inverted image ...

A convex lens of focal length 20 cm produces
images of the same magnification 2 when an
object is kept at two distances x1 and x2
(x1 > x2) from th...

A concave mirror for face viewing has focal
length of 0.4 m. The distance at which you hold
the mirror from your face in order to see your
image uprig...

A convex lens (of focal length 20 cm) and a
concave mirror, having their principal axes
along the same lines, are kept 80 cm apart from
each other. Th...

An upright object is placed at a distance of
40 cm in front of a convergent lens of focal
length 20 cm. A convergent mirror of focal
length 10 cm is p...

In figure, the optical fiber is $$l$$ = 2m long and
has a diameter of d = 20 μm. If a ray of light
is incident on one end of the fiber at angle
$$\the...

A plano-convex lens (focal length f2, refractive index $$\mu $$2, radius of curvature R) fits exactly into a plano-concave lens (focal length f1, refr...

Formation of real image using a biconvex lens is shown below :
If the whole set up is immersed in water without disturbing the object and the screen ...

A point source of light, S is placed at distance L in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walk...

What is the position and nature of image formed by lens combination shown in figure ? (f1, f2 are focal lengths)
...

A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the ...

An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the ...

The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following graphs is the cor...

The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea (7.8 mm). This surface sepa...

A plano convex lens of refractive index $$\mu $$1 and focal length ƒ1 is kept in contact with another plano concave lens of refractive index $$\mu $$2...

Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror (M1) and parallel to the second mirror (M2) is fina...

A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1...

A ray of light is incident at an angle of 60o on one face of a prism of angle 30o. The emergent ray of light makes an angle of 30o with incident ray....

A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of 10 cm. The separation between the two lens...

A planoconvex lens becomes an optical system of $$28$$ $$cm$$ focal length when its plane surface is silvered and illuminated from left to right as sh...

A particle is oscillating on the $$X$$-axis with an amplitude $$2$$ $$cm$$ about the point $${x_0} = 10\,cm,$$ with a frequency $$\omega $$. A concave...

In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it...

Let the refractive index of a denser medium with respect to a rarer medium be n12 and its critical angle be θC . At an angle of incidence A when light...

A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15cm from a converging
lens of magnitude of focal length 20cm. A beam...

To determine refractive index of glass slab using a travelling microscope, minimum number of readings required are :

A hemispherical glass body of radius 10 cm and refractive index 1.5 is silvered on its curved surface. A small air bubble is 6 cm below the flat surfa...

To find the focal length of a convex mirror, a student records the following data :
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{font-fam...

A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and aplane mirror are arranged as shown. For an object kept at a distance...

In an experiment for determination of refractive index of glass of a prism by $$i - \delta ,$$ plot it was found thata ray incident at angle $${35^ \c...

An observer looks at a distant tree of height $$10$$ $$m$$ with a telescope of magnifying power of $$20.$$ To the observer the tree appears:

Monochromatic light is incident on a glass prism of angle $$A$$. If the refractive index of the material of the prism is $$\mu $$, a ray, incident at ...

A thin convex lens made from crown glass $$\left( {\mu = {3 \over 2}} \right)$$ has focal length $$f$$. When it is measured in two different liquids ...

A green light is incident from the water to the air - water interface at the critical angle $$\left( \theta \right)$$. Select the correct statement.

Diameter of a plano-convex lens is $$6$$ $$cm$$ and thickness at the center is $$3mm$$. If speed of light in material of lens is $$2 \times {10^8}\,m/...

The graph between angle of deviation $$\left( \delta \right)$$ and angle of incidence $$(i)$$ for a triangular prism is represented by

An object $$2.4$$ $$m$$ in front of a lens forms a sharp image on a film $$12$$ $$cm$$ behind the lens. A glass plate $$1$$ $$cm$$ thick, of refracti...

Let $$x$$-$$z$$ plane be the boundary between two transparent media. Medium $$1$$ in $$z \ge 0$$ has a refractive index of $$\sqrt 2 $$ and medium $$2...

A car is fitted with a convex side-view mirror of focal length $$20$$ $$cm$$. A second car $$2.8m$$ behind the first car is overtaking the first car a...

An initially parallel cylindrical beam travels in a medium of refractive index $$\mu \left( I \right) = {\mu _0} + {\mu _2}\,I,$$ where $${\mu _0}$$ a...

An initially parallel cylindrical beam travels in a medium of refractive index $$\mu \left( I \right) = {\mu _0} + {\mu _2}\,I,$$ where $${\mu _0}$$ a...

In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is ad...

A transparent solid cylindrical rod has a refractive index of $${2 \over {\sqrt 3 }}.$$ It is surrounded by air. A light ray is incident at the mid-po...

A student measures the focal length of a convex lens by putting an object pin at a distance $$'u'$$ from the lens and measuring the distance $$'v'$$ o...

Two lenses of power $$-15$$ $$D$$ and $$+5$$ $$D$$ are in contact with each other. The focal length of the combination is

The refractive index of a glass is $$1.520$$ for red light and $$1.525$$ for blue light. Let $${D_1}$$ and $${D_2}$$ be angles of minimum deviation fo...

A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $${4 \over 3}$$ and th...

A thin glass (refractive index $$1.5$$) lens has optical power of $$-5$$ $$D$$ in air. Its optical power in a liquid medium with refractive index $$1....

A plano convex lens of refractive index $$1.5$$ and radius of curvature $$30$$ $$cm$$. Is silvered at the curved surface. Now this lens has been used ...

A light ray is incident perpendicularly to one face of a $${90^ \circ }$$ prism and is totally internally reflected at the glass-air interface. If the...

The image formed by an objective of a compound microscope is

To get three images of a single object, one should have two plane mirrors at an angle of

An astronomical telescope has a large aperture to

If two mirrors are kept at $${60^ \circ }$$ to each other, then the number of images formed by them is

Wavelength of light used in an optical instrument are $${\lambda _1} = 4000\mathop A\limits^ \circ $$ and $${\lambda _2} = 5000\mathop A\limits^ \ci...

Which of the following is used in optical fibres?