Optics PYQ

As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface.  If refractive index of the material of prism is $\sqrt{2}$, the angle $\theta$ of prism is.

A thin convex lens of focal length 5 cm and a thin concave lens of focal length 4 cm are combined together (without any gap) and this combination has magnification $m_{1}$ when an object is placed 10 cm before the convex lens. Keeping the positions of convex lens and object undisturbed a gap of 1 cm is introduced between the lenses by moving the concave lens away, which lead to a change in magnification of total lens system to $m_{2}$. The value of $\left|\frac{m_{1}}{m_{2}}\right|$ is $\_\_\_\_$.

The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is $\_\_\_\_$ cm.

Consider light travelling from a medium $A$ to medium $B$ separated by a plane interface. If the light undergoes total internal reflection during its travel from medium $A$ to $B$ and the speed of light in media $A$ and $B$ are $2.4 \times 10^{8} \mathrm{~m} / \mathrm{s}$ and $2.7 \times 10^{8} \mathrm{~m} / \mathrm{s}$, respectively, then the value of critical angle is :

A concave mirror of focal length $10$ cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is __________ cm.

In parallax method for the determination of focal length of a concave mirror, the object should always be placed:

In a Young double slit experiment, the wavelength of incident light is $6000$ Å, the separation between slits $S_1$ and $S_2$ is $5$ cm and the distance between slits plane and screen is $50$ cm, as shown in the figure below. If the resultant intensity at $P$ is equal to the intensity due to individual slits, the path difference between interfering waves is __________ Å. 

In two separate Young's double-slit experimental set-ups and two monochromatic light sources of different wavelengths are used to get fringes of equal width. The ratios of the slits separations and that of the wavelengths of light used are $2: 1$ and $1: 2$ respectively. The corresponding ratio of the distances between the slits and the respective screens ($D_{1} / D_{2}$) is $\_\_\_\_$.

When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted beam with respect to the normal is $\_\_\_\_$. $\left(\tan ^{-1}(1.52)=57.7^{\circ}\right.$, refractive indices of air and glass are 1.00 and 1.52, respectively.)

A ray of light passing through an equilateral prism is having velocity $2.12 \times 10^8$ m/s in the prism material, then the minimum angle of deviation is _________ degrees.

If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at $30$ cm above the paper. If the radius of curvature of the lens is $60$ cm then the refractive index of the lens material is $\dfrac{\alpha}{10}$. The value of $\alpha$ is _______.

In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and 5 cm. Total magnification obtained with this system for normal adjustment is $(5)^{k}$. The value of $k$ is $\_\_\_\_$.

Some distant star is to be observed by some telescope of diameter of objective lens $a$, at an angular resolution of $3.0\times 10^{-7}$ radian. If the wavelength of light from the star reaching the telescope is $500$ nm, the minimum diameter of the objective lens of the telescope is ________ cm. (nearest integer)

An unpolarized light of intensity $I_o$ passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is $0°$ and intensity of light emerged from analyser is $\dfrac{3}{8}I_o$, the angle of rotation of the light by the solution with respect to analyser is _______ degrees.

In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is $2.4$ $\mu$m. If the experiment is carried out in another medium having refractive index $1.2$, the fringe width will be _____ $\mu$m.

An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at $30°$ and $90°$, respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at $60°$ with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is ______.

In the Young's double slit experiment the intensity produced by each one of the individual slits is $I_{0}$. The distance between two slits is 2 mm. The distance of screen from slits is 10 m. The wavelength of light is $6000 \mathrm{~A}^{\circ}$. The intensity of light on the screen in front of one of the slits is $\_\_\_\_$.

Given below are two statements: Statement I: A plane wave after passing through prism remains as plane wave but passing through small pin hole may become spherical wave. Statement II: The curvature of a spherical wave emerging from a slit will increase for increasing slit width. In the light of the above statements, choose the correct answer from the options given below

In a double slit experiment, when one of the slits is covered by a transparent mica sheet of refractive index $1.56$, the central fringe shifts to the position of $7^{th}$ bright fringe, obtained with both slits uncovered. If the light source wavelength is $450$ nm, the thickness of mica sheet is $\alpha \times 10^{-9}$ m. The value of $\alpha$ is ______.

The wavelength of light, while it is passing through water is 540 nm. The refractive index of water is $4 / 3$. The wavelength of the same light when it is passing through a transparent medium having refractive index of $3 / 2$ is $\_\_\_\_$ nm.

A prism of angle $75^{\circ}$ and refractive index $\sqrt{3}$ is coated with thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be $\_\_\_\_$ ($\sin 15^{\circ}=0.25$ and $\sin 25^{\circ}=0.43$)

In a Young's double slit experiment set up, the two slits are kept 0.4 mm apart and screen is placed at 1 m from slits. If a thin transparent sheet of thickness $20 \mu \mathrm{~m}$ is introduced in front of one of the slits then center bright fringe shifts by 20 mm on the screen. The refractive index of transparent sheet is given by $\frac{\alpha}{10}$, where $\alpha$ is $\_\_\_\_$.