Ray Optics and ...

A beam of light is converging towards a point on the screen. If a plane parallel plate of glass of refraactive in $$\mu $$ and thickness t is introduced in the path of the beam, the convergent point is shifted  

Two identical thin isosceles prism of refracting angle 'A' and refractive index $$ \mu $$ are placed their bases touching each other. Two parallel rays of light are incident on this system as shown The distance of the point where the rays converge from the prism is: 

A ray of light makes normal incidence on the diagonal face of a right angled prism as shown in figure. If $$ \theta = 37^o $$, then the angle of deviation after second step (from AB) is (sin $$ 37^o = 3/5 $$ ) 

For water $$\mu = \dfrac{4}{3}$$ and the velocity of light in vacuum is $$3 \times 10^8 m/s$$, the time taken for light to travel a distance of $$450\ m$$ in water will be.

A convex lens of focal length $$\frac{1}{3}m$$ forms a real inverted image twice in size of the object. The distance of the object from the lens is 

A shallow glass dish is $$4.00\ cm$$ wide at the bottom, as shown in figure. When an observer's eye is positioned as shown, the observer sees the edge of the bottom of the empty dish. When this dish is filled with water, the observer sees the centre of the bottom of the dish. Find the height of the dish. $$(\mu_{w} = 4/3)$$.

A diverging meniscus of radii of curvatures $$25\ cm \ and \ 50 \ cm $$ has a refractive index $$1.5$$. Its focal length is :

Consider a hemisphere of radius R with centre of curvature at origin O, as shown. Refractive index of material of the hemisphere varies as $$\mu = \frac{2R}{2R-x}$$. Where x is x-coordinate of material point. A ray travelling in air in xy-plane is grazingly incident at O, as shown in the figure. Now answer the following question.
Deviation suffered by the ray just before it comes out of the hemispherical surface

A liquid of refractive index $$1.5$$ is poured into a cylindrical jar of radius $$20$$ cm up to a height of $$20$$ cm. A small bulb is lighted at the centre of the bottom of the jar. Find the area of the liquid surface through which the light of the bulb passes into air. 

A beam of light considering of red, green and blue colours is incident on an isosceles right angled prism as shown in the figure. the refractive indices of the material of the prism for red, green and blue colours are 1.39, 1.43 and 1.47 respectively. the prism will