Reflection of Light by Spherical Mirrors

An astronomical refractive telescope has an objective of focal length 20 m and an eyepiece of focal length 2 cm.

1. The length of the telescope tube is 20.02 m.
2. The magnification is 1000.
3. The image formed is inverted.
4. An objective of a larger aperture will increase the brightness and reduce chromatic aberration of the image.

A narrow pencil of parallel light is incident normally on a solid transparent sphere of radius r. What should be the refractive index is the pencil is to be focussed (a) at the surface of the sphere, (b) at the centre of the sphere.

A car is moving with at a constant speed of 60 km h^–1 on a straight road. Looking at the rear view mirror, the driver finds that the car following him is at a distance of 100 m and is approaching with a speed of 5 km h^–1. In order to keep track of the car in the rear, the driver begins to glance alternatively at the rear and side mirror of his car after every 2 s till the other car overtakes. If the two cars were maintaining their speeds, which of the following statement (s) is/are correct?

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

A spherical surface of radius 30 cm separates two transparent media A and B with refractive indices 1.33 and 1.48 respectively. The medium A is on the convex side of the surface. Where should a point object be placed in medium A so that the paraxial rays become parallel after refraction at the surface?

Can mirrors give rise to chromatic aberration?

A converging lens has a focal length of 10 cm in air. It is made of a material with a refractive index of 1.6. If it is immersed in a liquid of refractive index 1.3, find its new focal length.

A lens of focal length f is divided into two equal parts and then these parts are put in a combination as shown in the figure below.

1. What is the focal length of L₁?
2. What is the focal length of the final combination?