Physics Ray Optics and Optical Instruments

A light ray enters a solid glass sphere of refractive index μ = √3 at an angle of incidence 60°. The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is

Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1 kg–m² and 10 rads⁻¹ respectively while those for the second one are 0.2 kg–m² and 5 rads⁻¹ respectively. At some instant, they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is:

A spherical mirror is obtained as shown in the figure from a hollow glass sphere. if an object is positioned infront of the mirror, what will be the nature and magnification of the image of the object? (Figure drawn as schematic and not to scale)

A point like object is placed at a distance of 1 m in front of convex lens of focal length 0.5 m. A plane mirror is placed at a distance of 2 m behind the lens. The position and nature of the final image formed by the system is:

A prism of angle A = 1° has a refractive index µ = 1.5. A good estimate for the minimum angle of deviation (in degrees) is close to N/10. Value of N is 

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 $$ $30\mathrm{c}\mathrm{m}$ and the refractive index of the lens material is 1.5 , then the focal length of the lens (in $\mathrm{c}\mathrm{m}$ $$ ) is(Ray Optics)

The magnifying power of a telescope with tube length $60\mathrm{c}\mathrm{m}$ $$ is 5 . What is the focal length of its eye piece?

If we need a magnification of 375 from a compound microscope of tube length $150\mathrm{m}\mathrm{m}$ $$ and an objective of focal length $5\mathrm{m}\mathrm{m}$ $$ , the focal length of the eye piece should be close to

A thin lens made of glass (refractive index $=1.5$ ) of focal length $f=16\mathrm{c}\mathrm{m}$ is immersed in a liquid of refractive index 1.42. If its focal length in liquid is $f_{\mathcal{l}}$ , then the ratio $f_{\mathcal{l}}$  /f is closest to the integer:

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