Wave Optics · Physics · Class 12

(a) In a diffraction experiment, the slit is illuminated by light of wavelength 600 nm . The first minimum of the pattern falls at $\theta=30^{\circ}$. Calculate the width of the slit.

OR

(b) In a Young's double-slit experiment, two light waves, each of intensity $I_0$, interfere at a point, having a path difference $\frac{\lambda}{8}$ on the screen. Find the intensity at this point.

(a) (i) (1) What are coherent sources? Why are they necessary for observing a sustained interference pattern?

(2) Lights from two independent sources are not coherent. Explain.

(ii) Two slits 0.1 mm apart are arranged 1.20 m from a screen. Light of wavelength 600 nm from a distant source is incident on the slits.

(1) How far apart will adjacent bright interference fringes be on the screen?

(2) Find the angular width (in degree) of the first bright fringe.

OR

(b) (i) Define a wave front. An incident plane wave falls on a convex lens and gets refracted through it. Draw a diagram to show the incident and refracted wave front.

(ii) A beam of light coming from a distant source is refracted by a spherical glass ball (refractive index 1.5) of radius 15 cm . Draw the ray diagram and obtain the position of the final image formed.

(a) (i) A plane light wave propagating from a rarer into a denser medium, is incident at an angle $i$ on the surface separating two media. Using Huygen's principle, draw the refracted wave and hence verify Snell's law of refraction.

(ii) In a Young's double slit experiment, the slits are separated by 0.30 mm and the screen is kept 1.5 m away. The wavelength of light used is 600 nm . Calculate the distance between the central bright fringe and the $4^{\text {th }}$ dark fringe.

OR

(b) (i) Discuss briefly diffraction of light from a single slit and draw the shape of the diffraction pattern.

(ii) An object is placed between the pole and the focus of a concave mirror. Using mirror formula, prove mathematically that it produces a virtual and an enlarged image.

What happens to the interference pattern when two coherent sources are

(a) infinitely close, and

(b) far apart from each other

(a) (i) State Huygen's principle. With the help of a diagram, show how a plane wave is reflected from a surface. Hence, verify the law of reflection.

(ii) A concave mirror of focal length $$12 \mathrm{~cm}$$ forms a three times magnified virtual image of an object. Find the distance of the object from the mirror.

OR

(b) (i) Draw a labelled ray diagram showing the image formation by a refracting telescope. Define its magnifying power. Write two limitations of a refracting telescope over a reflecting telescope.

(ii) The focal lengths of the objective and the eyepiece of a compound microscope are $$1.0 \mathrm{~cm}$$ and $$2.5 \mathrm{~cm}$$ respectively. Find the tube length of the microscope for obtaining a magnification of 300.

(a) A plane wave-front propagating in a medium of refractive index '$$\mu_1$$' is incident on a plane surface making an angle of incidence (i). It enters into a medium of refractive index $$\mu_2\left(\mu_2>\mu_1\right)$$. Use Huygen's construction of secondary wavelets to trace the retracted wave-front. Hence, verify Snell's law of refraction.

OR

Using Huygen's construction, show how a plane wave is reflected from a surface. Hence, verify the law of reflection.

A Young's double-slit experimental set up is kept in a medium of refractive index $\left(\frac{4}{3}\right)$. Which maximum in this case will coincide with the $6^{\text {th }}$ maximum obtained if the medium is replaced by air?

Assertion (A): In a Young's double-slit experiment, interference pattern is not observed when two coherent sources are infinitely close to each other.

Reason (R): The fringe width is proportional to the separation between the two sources.

A beam of light travels from air into a medium. Its speed and wavelength in the medium are $$1.5 \times 10^8\mathrm{ms}^{-1}$$ and $$230 \mathrm{~nm}$$ respectively. The wavelength of light in air will be

Assertion (A) : In Young's double slit experiment all fringes are of equal width.

Reason (R) : The fringe width depends upon wavelength of light $$(\lambda)$$ used, distance of screen from plane of slits (D) and slits separation (d).

In a Young's double-slit experiment, the screen is moved away from the plane of the slits. What will be its effect on the following?

(i) Angular separation of the fringes.

(ii) Fringe-width.

According to Huygens principle, the amplitude of secondary wavelets is