(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.

(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.