A plane-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices μ₁ and μ₂ and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is:

For a normal eye, the cornea of eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be

When a biconvex lens of glass having refractive index 1.47 is dipped in a liquid, it acts as a plane sheet of glass. This implies that the liquid must have refractive index 

A ray of light is incident at an angle of incidence, i, on one face of a prism of angle A (assumed to be small) and emerges normally from the opposite face.If the refractive index of the prism is $\mu ,$ the angle of incidence i, is nearly equal to

A concave mirror of focal length $f_1$ is placed at a distance of d from a convex lens of focal length $f_2.$ A beam of light coming from infinity and falling on this convex lens concave mirror combination returns to infinity. The distance d must be equal to-

The magnifying power of a telescope is 9. When it is adjusted for parallel rays the distance between the objective and eyepiece is 20cm. The focal length of lenses are 

For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index

Converging rays are incident on a convex lens, the image formed

A biconvex lens of refractive index 1.5, has a radius of curvature of magnitude 20 cm. Which one of the following options describes best the image formed of an object of height 2 cm placed 30 cm from the lens?

Which of the following is not due to total internal reflection?

A thin prism of angle $15°$ made of glass of refractive index ${\mathrm{\mu }}_1=1.5$ is combined with another prism of glass of refractive index ${\mathrm{\mu }}_2=1.75.$ The combination of the prism produces dispersion without deviation. The angle of the second prism should be 

A converging beam of rays is incident on a diverging lens. Having passed though the lens the rays intersect at a point 15cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5cm closer to the lens. The focal length of the lens is:

A ray of light traveling in a transparent medium of refractive index $\mu$ falls, on a surface separating the medium from the air at an angle of incidence of 45$°$.For which of the following value of $\mu$ the ray can undergo total internal reflection?

A lens having focal length f and aperature of diameter d forms an image of intensity I. Aperture of diameter $\frac{d}{2}$ in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively

(a) f and $\frac{1}{4}$                                      (b) $\frac{3f}{4}and \frac{I}{2}$

(c) f and $\frac{3I}{4}$                                     (d) $\frac{f}{2}and \frac{I}{2}$

The speed of light in media ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ is $1.5\times {10}^8 \mathrm{m}/\mathrm{s}$ and $2.0\times {10}^8 \mathrm{m}/\mathrm{s}$ respectively. A ray of light enters from medium ${\mathrm{M}}_1$ to ${\mathrm{M}}_2$ at an incidence angle i. If the ray suffers total internal reflection, the value of i is

A ray of light is incident on a $60°$ prism at the minimum deviation position. The angle of refraction at the first face (ie, incident face) of the prism is 

Two thin lenses of focal length $f_1 and f_2$ are in contact and coaxial. The power of the combination is 

The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is 30°. One of the two refracting surfaces of the prism is made a mirror inwards, by a silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if the angle of incidence on the prism is:

$$\begin{gathered} 1. 60° \\ 2. 45° \\ 3. 30° \\ 4. \mathrm{Zero} \end{gathered}$$

An object is placed at a distance of 40 cm from a concave mirror of a focal length of 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be:

A person can see clearly objects only when they lie between 50 cm and 400 cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be

An astronomical refracting telescope will have large angular magnification and high angular resolution when it has an objective lens of:-

A beam of light consisting of red, green, and blue colors is incident on a right-angled prism. The refractive index of the material of the prism for the red, green, and blue wavelengths is 1.39, 1.44, and 1.47 respectively. 
 
The prism will :

Two identical thin plano-convex glass lenses (refractive index = 1.5) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is: