Ray Optics and ...

An object is placed at a distance of 1.5 m from a screen and a convex lens is interposed between them. The magnification produced is 4. The focal length of the lens is :

A sphere of radius $$R$$ is placed in air such that its centre is at origin. A ray of light traveling along $$y =  + \dfrac{{\sqrt 3 }}{2}R$$ (in x-y plane) is incident on this sphere.

If ray travels through sphere as shown in figure, then:

A ray of light enters a spherical drop of water of refractive index $$\mu$$ as shown in the figure. The angle $$\phi$$ for which minimum deviation is produced will be given by :

One end of a glass rod of refractive index $$n=1.5$$ is spherical surface of radius of curvature $$R$$. The centre of the spherical surface lies inside the glass. A point object placed in air on the axis of the rod at the point $$P$$ has its real image inside glass at the point Q (see figure). A line joining the points P and Q cuts the surface at O such that $$OP=2OQ$$. The distance PO is

A light ray passes through a prism with an apex angle $$30^\circ$$ as shown in figure. Incident medium is air. Critical angle for air prism interface is $$42^\circ$$. As angle 'i' increases from zero to  $$90^\circ$$ in anti clock wise sense, angle of emergence changes. Which of following options is/are correct, when $$i = 90^\circ$$.
[Given $$\sin \ 42^\circ \cong 0.670; \sin \ 12^\circ \cong 0.21; \sin \ 18^\circ \cong 0.313.$$]

An achromatic combination is made by combining 2 prisms as shown:-
If $$\omega_1 > \omega_2$$, then 

A point object $$O$$ is placed in front of a glass rod having a spherical end of radius of curvature $$30\ cm$$. The image would be formed at :

A spherical refractive surface of radius $$10$$ cm separates two media of refractive indices $$ \mu = 1$$ and $$ \mu = 3/2$$ respectively. A point object P starts from rest at $$t = 0$$ with an acceleration $$2 \ cm s^{-2}$$. Find the speed of image at $$t =1$$ s.

A light ray is incident normally on one of the refracting faces of a prism and just emerges  out grazing the second surface. The relation between angle of the prism and its critical angle is

A double convex lens of focal length $$30cm$$ is made of glass. When it is immersed in a liquid of refractive index $$1.5$$, the focal length is found to be $$120cm$$. The critical angle between glass and the liquid is