Reflection of Light by Spherical Mirrors

A double convex lens is made of a glass of refractive index 1.55, with both faces of the same radius of curvature. Find the radius of curvature required, if the focal length is 20 cm.

State how the focal length of a glass lens (Refractive Index 1.5) changes when it is completely immersed in: 

(i) Water (Refractive Index 1.33)
(ii) A liquid (Refractive Index 1.65)

A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.

Light is incident from glass (μ = 1.5) to air. Sketch the variation of the angle of deviation δ with the angle of incident i for 0 < i < 90°.

With the help of a ray diagram, obtain the relation between its focal length and radius of curvature.

(i) Consider a thin lens placed between a source (S) and an observer (O) (Figure). Let the thickness of the lens vary as `w(b) = w_0 - b^2/α`, where b is the verticle distance from the pole. `w_0` is a constant. Using Fermat’s principle i.e. the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converge at a point O on the axis. Find the focal length.

(ii) A gravitational lens may be assumed to have a varying width of the form

`w(b) = k_1ln(k_2/b) b_("min") < b < b_("max")`

= `k_1ln (K_2/b_("min")) b < b_("min")`

Show that an observer will see an image of a point object as a ring about the center of the lens with an angular radius

`β = sqrt((n - 1)k_1 u/v)/(u + v)`

In image formation from spherical mirrors, only paraxial rays are considered because they

A converging lens of focal length 40 cm is kept in contact with a diverging lens of focal length 30 cm. Find the focal length of the combination .