A ray of light incidents at an angle of $9.3^{\circ}$ on one face of a small angle prism of refracting angle $6^{\circ}$. If the ray of light emerges normally from the second face, the refractive index of the material of the prism is

If the distances of the object and its real image from the principal focus of a concave mirror are 16 cm and 9 cm respectively, then the focal length of the mirror is

If the angle of minimum deviation produced by an equilateral prism is equal to the angle of the prism, then the refractive index of the material of the prism is nearly

A cassegrain telescope uses two mirrors of radii of curvature 25 cm and 16 cm separated by a distance of 2.5 cm . The position of the final image of an object at infinity is

A convex lens of radii of curvature 6 cm and 12 cm is immersed in a liquid of refractive index 1.3. If the refractive index of the material of the lens is 1.5 , then the focal length of the lens when immersed in the liquid is

When unpolarised light from air incidents on the surface of a medium of refractive index $\sqrt{3}$, then the reflected light is totally polarised. The angle of refraction is

An object of height 3.6 cm is placed normally on the principal axis of a concave mirror of radius of curvature 30 cm . If the object is at a distance of 10 cm from the principal focus of the mirror, then the height of the real image formed due to the mirror is

Monochromatic light of wavelength $6000 \mathop {\rm{A}}\limits^{\rm{o}} $ incidents on a small angled prism. If the angle of the prism is $6^{\circ}$, the refractive indices of the material of the prism for violet and red lights are respectively 1.52 and 1.48 , then the angle of dispersion produced for this incident light is

A compound microscope has an objective of focal length 1.25 cm and an eyepiece of focal length 5 cm separated by a distance of 7.5 cm . The total magnification produced by the microscope when the final image forms at infinity is

The property of light that explains the formation of coloured images due to thick lenses is

The angle of a prism made of a material of refractive index $\sqrt{2}$ is $90^{\circ}$. The angle of incidence for a light ray on the first face of the prism such that the light ray suffers total internal reflection at the second face is

The total magnification produced by a compound microscope is 24 when the final image is formed at the least distance of distinct vision. If the focal length of the eyepiece is 5 cm , the magnification produced by the objective is

The focal lengths of the objective and the eyepiece of a compound microscope are 2 cm and 3 cm respectively and the distance between them is 15 cm . The final image formed by the eyepiece is at infinity. The distances of the object and the image produced by the object from the objective lens are respectively.

Two convex lenses of focal lengths 20 cm and 30 cm are placed in contact with each other co-axially. The focal length of the combination is

A convex lens forms a real image of a point object placed on its principal axis. If the upper half of the lens is painted black, then

Refractive index of a medium is $\mu$. If the angle of incidence is twice that of the angle of refracation, then the angle of incidence is

The angles of incidence and emergence of a light ray passing through a prism of angle $A$ are $i$ and $e$ respectively. The total deviation produced by the prism is

A convex lens of focal length 25 cm and made of glass with refractive index 1.5 is immersed in water. the absolute change in focal length of the glass is [use refractive index of water $=4 / 3$ ]

What is the refractive index of the material of a double convex lens having radii of curvature of 5 cm and 10 cm and focal length of $\frac{20}{3} \mathrm{~cm}$

A spherical glass is attached to a rigid wall as shown in the figure. An observer located at point $O$ is looking at a point $A$ on the wall. The refractive index of the glass is 1.5 and that of air is 1.0 . The distances are $O A=8 \mathrm{~cm}$, $X A=3 \mathrm{~cm}$. If the radius of curvature of spherical glass surface is $R=5 \mathrm{~cm}$, then the apparent distance of $A$ from observer $O$ is

A light ray travels from a medium with refractive index $n_1$ to another medium of refractive index $n_2$. If $n_1=2$ and $n_2=\sqrt{3}$, then find the critical angle.

A convex lens focusses an object 20 cm from it on a screen placed 5 cm away from it. A glass plate (refractive index $=7 / 5$ ) of thickness 1.4 cm is inserted between the lens and the screen. What is the distance of the object from the lens, so that its image is again focused on the screen?

A lens is made of glass having an index of refraction 1.5 . One side of the lens is flat and the other side is convex with a radius $R$. If an object is placed 60 cm , towards the convex side of the lens, the image is formed at

A prism is made of a glass having refractive index $\sqrt{2}$. If the angle of minimum deviation is equal to angle of the prism, then the angle of prism is

A thin glass prism of angle $9^{\circ}$ with refractive index 1.4 is combined with another glass prism of refractive index 1.6 as shown in the figure. The combination of the prism provides dispersion without deviation. Determine the angle $(A)$ of the second prism.

A short straight object of length $l$ lies along the central axis of a spherical concave mirror, at a distance $X$ from the mirror. The focal length of the mirror is $F$. If the length of the image in the mirror is $l^{\prime}$, then ratio $\left(\frac{l^{\prime}}{l}\right)$ is (assume, $l \ll X$ and $l \ll F$ )

Consider a glass prism immersed in a liquid as shown below. The refractive index of glass and liquid is 1.5 and 1.2, respectively. A ray of light enters the prism perpendicular to the face $A B$. The largest value of angle $\theta$ is, if the ray is totally reflected at the face $A C$, then

A telescope has an objective of focal length 100 cm and an eye-piece of focal length 5 cm . The magnifying power of the telescope is

A convex lens and a concave lens, each with focal length of 4 cm are separated by a distance of 6 cm along their axis. An object is placed 8 cm before the convex lens. The distance between the object and its image is

If the image of an object is at the focal point $f$ to the right side of a convex lens, the position of the object on the left of the lens is at