Ray optics practice · Mixed difficulty

A ray enters a glass slab at an angle $\alpha$ from air and the refractive index varies along the slab as $\mu=\mu_0-k t^2$ where $t$ is the distance measured along the normal. $\mu_0$ and $k$ are positive constants. If the glass slab is sufficiently thick, how far along the normal will the ray go before it reflects back?

In an equilateral prism if incident angle is ${45^ \circ }$ then minimum deviation is

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

Focal length of a plane mirror is

Assertion (A): When a wave travels from a denser to a rearer medium its amplitude increases.

Reason (R): In a rarer medium speed of wave is more.

A ray of light enters a rectangular glass slab of refractive index $\sqrt{3}$ at angle of incidence $60^{\circ}$. It ravels a distance of $10 \mathrm{~cm}$ inside the slab and emerges out of the slab. The perpendicular distance between the incident and the emergent rays is

In the visible region the dispersive powers and the mean angular deviations for crown and flint glass prisms are $\omega ,\,\,\omega '$ and $d,\,\,d'$ respectively. The condition for getting deviation without dispersion when the two prisms are combined is

A beaker containing a liquid appears to be half when it is actually two third full.The refractive index of liquid

The instrument used by doctors for endoscopy works on the principle of

Dark lines on solar spectrum are due to

What cause chromatic aberration?

Given below are two statements:

Statement I: When the white light passed through a prism, the red light bends lesser than yellow and violet.

Statement II: The refractive indices are different for different wavelengths in dispersive medium.
In the light of the above statements, choose the correct answer from the options given below:

Assertion: A double convex lens $(\mu=1.5)$ has focal length $10 \mathrm{~cm}$. When the lens is immersed in water $(\mu=4 / 3)$ its focal length becomes $40 \mathrm{~cm}$.
Reason: $\frac{1}{f}=\frac{\mu_1-\mu_m}{\mu_m}\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

In the position of minimum deviation when a ray of yellow light passes through the prism, then its angle of incidence is

In an experiment to measure focal length $(f)$ of convex lens, the least counts of the measuring scales for the position of object $(u)$ and for the position of image $(v)$ are $\Delta u$ and $\Delta v$, respectively. The error in the measurement of the focal length of the convex lens will be:

The image formed by an objective of a compound microscope is

A parallel beam of white light falls on a convex lens. Images of blue, yellow and red light are formed on other side of the lens at a distance of $0.20\,\,m,\,\,0.205\,\,m$ and $0.214\,\,m$ respectively. The dispersive power of the material of the lens will be

The focal length $f$ is related to the radius of curvature $r$ of the spherical convex mirror by

A normally incident ray reflected at an angle of ${90^0}$. The value of critical angle is

The plane face of a planoconvex lens is silvered. If $\mathrm{\mu }$ be the refractive index and $R$, the radius of curvature of curved surface, then the system will behave like a concave mirror of radius of curvature

Assertion : A man inside the water see a tree, the tree will appear long than its original length.

Reason : There is difference in the refractive index of air and water.

A biconvex lens form a real image of an object placed perpendicular to its principal axis. Suppose the radii of curvature of the lens tend to infinity. Then the image would

The least angle of deviation for a glass prism is equal to its refracting angle. The refractive index of glass is $\mathrm{1}\mathrm{.5}$. Then the angle of prism is

An object is lying at a distance of 90 cm from a concave mirror of focal length 30 cm. The position and nature of image formed by it will be

Assertion (A): A convex mirror cannot form real images.

Reason (R): Convex mirror converges the parallel rays that are incident on it

A convex lens of focal length $40 \mathrm{~cm}$ forms an image of an extended source of light on a photoelectric cell. A current $I$ is produced. The lens is replaced by another convex lens having the same diameter but focal length $20 \mathrm{~cm}.$ The photoelectric current now is:

A double convex lens made out of glass (refractive index $\mathrm{\mu } = 1.5)$ has both radii of curvature of magnitudes $\mathrm{20 cm}$. Incident light rays parallel to the axis of this lens will converge at a distance $d$ such that

What should be the maximum acceptance angle at the aircore interface of an optical fibre if ${n_1}$ and ${n_2}$ are the refractive indices of the core and the cladding, respectively

Red light is incident on a converging lens of focal length $f$. When we replace this red light with blue then the focal length

The number of lenses in a terrestrial telescope is