A microscope has an objective of focal length 2 cm , eyepiece of focal length 4 cm and the tube length of 40 cm . If the distance of distinct vision of eye is 25 cm , the magnification in the microscope is

In a certain camera, a combination of four similar thin convex lenses are arranged axially in contact. Then the power of the combination and the total magnification in comparison to the power ( $p$ ) and magnification ( $m$ ) for each lens will be, respectively

Given below are two statements:

Statement I : Image formation needs regular reflection and/or refraction.

Statement II : The variety in colour of objects we see around us is due to the constituent colours of the light incident on them.

In the light of the above statements, choose the most appropriate answer from the options given below :

A light ray enters through a right angled prism at point $$P$$ with the angle of incidence $$30^{\circ}$$ as shown in figure. It travels through the prism parallel to its base $$B C$$ and emerges along the face $$A C$$. The refractive index of the prism is:

A small telescope has an objective of focal length $$140 \mathrm{~cm}$$ and an eye piece of focal length $$5.0 \mathrm{~cm}$$. The magnifying power of telescope for viewing a distant object is:

A lens is made up of 3 different transparent media as shown in figure. A point object O is placed on its axis beyond $$2f$$. How many real images will be obtained on the other side?

$$\epsilon_0$$ and $$\mu_0$$ are the electric permittivity and magnetic permeability of free space respectively. If the corresponding quantities of a medium are $$2 ~\epsilon_0$$ and $$1.5 ~\mu_0$$ respectively, the refractive index of the medium will nearly be :

A horizontal ray of light is incident on the right angled prism with prism angle $$6^{\circ}$$. If the refractive index of the material of the prism is 1.5 , then the angle of emergence will be:

An object is mounted on a wall. Its image of equal size is to be obtained on a parallel wall with the help of a convex lens placed between these walls. The lens is kept at distance x in front of the second wall. The required focal length of the lens will be :

Light travels a distance $$\mathrm{x}$$ in time $$t_{1}$$ in air and $$10 \mathrm{x}$$ in time $$t_{2}$$ in another denser medium. What is the critical angle for this medium?

In the figure shown here, what is the equivalent focal length of the combination of lenses (Assume that all layers are thin) ?

Two thin lenses are of same focal lengths $$(f)$$, but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be :

During a cloudy day, a primary and a secondary rainbow may be created, then the :

An astronomical refracting telescope is being used by an observer to observe planets in normal adjustment. The focal lengths of the objective and eye piece used in the construction of the telescope are 20 m and 2 cm respectively. Consider the following statements about the telescope :

(a) The distance between the objective and eye piece is 20.02 m

(b) The magnification of the telescope is ($$-$$) 1000

(c) The image of the planet is erect and diminished

(d) The aperture of eye piece is smaller than that of objective

The correct statements are :

A biconvex lens has radii of curvature, 20 cm each. If the refractive index of the material of the lens is 1.5, the power of the lens is

A light ray falls on a glass surface of refractive index $$\sqrt3$$, at an angle 60$$^\circ$$. The angle between the refracted and reflected rays would be

Two transparent media A and B are separated by a plane boundary. The speed of light in those media are 1.5 $$\times$$ 10⁸ m/s and 2.0 $$\times$$ 10⁸ m/s, respectively. The critical angle for a ray of light for these two media is