The refractive index of water is 4/3. Obtain the value of the semivertical angle of the cone within which the entire outside view would be confined for a fish under water. Draw an appropriate ray diagram

A lens forms a real image of an object. The distance of the object to the lens is 4 cm and the distance of the image from the lens is v cm. The given graph shows the variation of v with u.
(i) What is the nature of the lens?
(ii) Using this graph, find the focal length of this lens.

A ray of light passes through an equilateral glass prism, such that the angle of incidence is equal to the angle of emergence. If the angle of emergence is ¾ times the angle of the prism, Calculate the refractive index of the glass prism

(a) A point object is placed in front of a double convex lens (of refractive index n =n₂/n₁ with respect air) with its spherical faces of radii of curvature R₁ and R_2.. Show the path of rays due to surface to obtain the formation of the real image of the object.
Hence obtain the lens maker's formula for a thin lens.
(b) A double convex lens having both faces of the same radius of curvature has refractive index 1.55. Find out the radius of curvature of the lens required to get the focal length of 20 cm.

Light of wavelength \(5000\overset { \circ }{ A } \) falls on a plane reflecting surface. What are the wavelength and frequency of reflected light? For what angle of incidence is the reflected ray normal to the incident ray?

A 5 cm long needle is placed 10 cm from a convex mirror of focal length 40 cm. Find the position, nature and size of image of the needle. What happens to the size of image when needle is moved farther away from the mirror?

A ray of light is incident at an angle of \(45°\) on one face of a rectangular glass slab of thickness 10 cm and refractive index 1.5. Calculate the lateral shift produced.

In a single-slit diffraction experiment, the first minimum for red light coincides with the first maximum of some other wavelength.\(\lambda '\) Calculate \(\lambda '\)

Calculate the critical angle for total internal reflection of light travelling from (i) water into air (ii) glass into water. Given, \(^{ a }{ \mu }_{ w }=1.33\) and \(^{ a }{ \mu }_{ g }=1.5\)

A telescope has an objective of diameter 60 cm. The focal lengths of the objective and eyepiece are 2.0m and 1.0cm. respectively. The telescope is directed to view two distant almost point sources of light. The sources are roughly at the same distance along the line of sight, but separated transverse to the line of sight by a distance of \({ 10 }^{ 10 }m\) Will the telescope resolve the two objects.

A radar wave has a frequency of.\(8.1\times { 10 }^{ 9 }Hz\) The reflected wave from an airplane shows a frequency difference of \(2.7\times { 10 }^{ 3 }Hz\)on the higher side. Calculate the velocity of an airplane in the line of sight.

The spectral line for a given element in light received from a distant star is shifted towards the longer wavelength by 0.032%. Deduce the velocity of star in the line of sight.