Geometrical Optics · Physics · Class 12

The focal lengths of the objective and the eyepiece of a compound microscope are 1 cm and 2 cm respectively. If the tube length of the microscope is 10 cm , the magnification obtained by the microscope for most suitable viewing by relaxed eye is

A ray of monochromatic light propagating in air, is incident on the surface of water. Which of the following will be the same for the reflected and refracted rays?

A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm . Calculate its magnifying power in normal adjustment and the distance of the image formed by the objective.

A prism is an optical medium bounded by three refracting plane surfaces. A ray of light suffers successive refractions on passing through its two surfaces and deviates by a certain angle from its original path. The refractive index of the material of the prism is given by $\mu=\sin \left(\frac{A+\delta_m}{2}\right) / \sin \frac{A}{2}$. If the angle of incidence on the second surface is greater than an angle called critical angle, the ray will not be refracted from the second surface and is totally internally reflected.

(i) The critical angle for glass is $\theta_1$ and that for water is $\theta_2$. The critical angle for glass-water surface would be (given ${ }_a \mu_g=1.5,{ }_a \mu_w=1.33$ )

(A) less than $\theta_2$

(B) between $\theta_1$ and $\theta_2$

(C) greater than $\theta_2$

(D) less than $\theta_1$

(ii) When a ray of light of wavelength $\lambda$ and frequency $v$ is refracted into a denser medium

(A) $\lambda$ and $v$ both increase.

(B) $\lambda$ increases but $v$ is unchanged.

(C) $\lambda$ decreases but $v$ is unchanged.

(D) $\lambda$ and $v$ both decrease.

(iii) (a) The critical angle for a ray of light passing from glass to water is minimum for

(A) red colour

(B) blue colour

(C) yellow colour

(D) violet colour

OR

(b) Three beams of red, yellow and violet colours are passed through a prism, one by one under the same condition. When the prism is in the position of minimum deviation, the angles of refraction from the second surface are $r_{\mathrm{R}}, r_Y$ and $r_{\mathrm{V}}$ respectively. Then

(A) $r_V< r_Y

(B) $r_Y< r_R

(C) $r_R< r_Y

(D) $r_{\mathrm{R}}=r_{\mathrm{Y}}=r_{\mathrm{V}}$

(iv) A ray of light is incident normally on a prism ABC of refractive index $\sqrt{ } 2$, as shown in figure. After it strikes face AC, it will

(A) go straight undeviated

(B) just graze along the face AC

(C) refract and go out of the prism

(D) undergo total internal reflection

(a) (i) Draw a ray diagram to show the working of a compound microscope. Obtain the expression for the total magnification for the final image to be formed at the near point.

(ii) In a compound microscope an object is placed at a distance of $$1.5 \mathrm{~cm}$$ from the objective of focal length $$1.25 \mathrm{~cm}$$. If the eye-piece has a focal length of $$5 \mathrm{~cm}$$ and the final image is formed at the near point, find the magnifying power of the microscope.

OR

(b) (i) Draw a ray diagram for the formation of image of an object by an astronomical telescope, in normal adjustment. Obtain the expression for its magnifying power.

(ii) The magnifying power of an astronomical telescope in normal adjustment is 2.9 and the objective and the eyepiece are separated by a distance of $$150 \mathrm{~cm}$$. Find the focal lengths of the two lenses.

A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Considering image formation by a single spherical surface successively at the two surfaces of a lens, lens maker's formula is obtained. It is useful to design lenses of desired focal length using surfaces of suitable radii of curvature. This formula helps us obtain a relation between $$u, v$$ and $$f$$ for a lens. Lenses form images of objects and they are used in a number of optical devices, for example microscopes and telescopes.

(i) An object AB is kept in front of a composite convex lens, as shown in figure. Will the lens produce one image? If not, explain.

(ii) A real image of an object formed by a convex lens is observed on a screen. If the screen is removed, will the image still be formed? Explain.

(iii) A double convex lens is made of glass of refractive index 1.55 with both faces of the same radius of curvature. Find the radius of curvature required if focal length is $$20 \mathrm{~cm}$$.

OR

(iii) Two convex lenses A and B of focal lengths $$15 \mathrm{~cm}$$ and $$10 \mathrm{~cm}$$ respectively are placed coaxially '$$d$$' distance apart. A point object is kept at a distance of $$30 \mathrm{~cm}$$ in front of lens A. Find the value of '$$d$$' so that the rays emerging from lens $B$ are parallel to its principal axis.

In the given figure the radius of curvature of curved face in the plano-convex and the plano-concave lens is $$15 \mathrm{~cm}$$ each. The refractive index of the material of the lenses is 1.5. Find the final position of the image formed.

Define critical angle for a given pair of media and total internal reflection. Obtain the relation between the critical angle and refractive index of the medium.