Optics PYQ — Page 3

Refer the figure given below. $\mu_1$ and $\mu_2$ are refractive indices of air and lens material. The height of image will be _______ cm. 

A telescope with objective diameter $R$ is used to observe a distant star emitting light of wavelength $500$ nm, at a resolution of $5 \times 10^{-7}$ radian. The value of $R$ is _____ cm.

The magnitudes of power of a biconvex lens (refractive index 1.5) and that of a plano-concave lens (refractive index $=1.7$) are same. If the curvature of planoconcave lens exactly matches with the curvature of back surface of the biconvex lens, then ratio of radius of curvature of front and back surface of the biconvex lens is $\_\_\_\_$.

A thin biconvex lens is prepared from the glass ($\mu=1.5$) both curved surfaces of which have equal radii of $20$ cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of ________ cm.

A spherical interface lens of radius $R$ separates two media of refractive indices $1$ and $1.4$ respectively as shown in the figure below. A point source is placed at a distance of $4R$ in front of spherical interface. The magnitude of the magnification of point source image is _______. 

Distance between an object and three times magnified real image is 40 cm. The focal length of the mirror used is $\_\_\_\_$ cm.

An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and $2 \sqrt{3}$ (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is $\_\_\_\_$.

For a thin symmetric prism made of glass (refractive index $1.5$), the ratio of incident angle and minimum deviation will be _______.

Five persons $\mathrm{P}_{1}, \mathrm{P}_{2}, \mathrm{P}_{3}, \mathrm{P}_{4}$ and $\mathrm{P}_{5}$ recorded object distance $(\mathrm{u})$ and image distance (v) using same convex lens having power +5 D as $(25,96),(30,62),(35,37),(45,35)$ and $(50,32)$ respectively. Identify correct statement

In Young's double slit experiment, the fringe width is β. If the wavelength of light is doubled and the slit separation is halved, the new fringe width is:

The exit surface of a prism with refractive index $n$ is coated with a material having refractive index $\frac{n}{2}$. When this prism is set for minimum angle of deviation, it exactly meets the condition of critical angle. The prism angle is $\_\_\_\_$.

Given a thin convex lens (refractive index $\mu_2$ ), kept in a liquid (refractive index $\mu_1, \mu_1 \lt \mu_2$ ) having radii of curvatures $\left|R_1\right|$ and $\left|R_2\right|$. Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm , at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is :

A lens having refractive index 1.6 has focal length of 12 cm , when it is in air. Find the focal length of the lens when it is placed in water. (Take refractive index of water as 1.28)

A container contains a liquid with refractive index of 1.2 up to a height of 60 cm and another liquid having refractive index 1.6 is added to height H above first liquid. If viewed from above, the apparent shift in the position of bottom of container is 40 cm. The value of H is ______ cm. (Consider liquids are immisible)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R) Assertion (A) : Refractive index of glass is higher than that of air. Reason ( $\mathrm{R}$) : Optical density of a medium is directly proportionate to its mass density which results in a proportionate refractive index. In the light of the above statements, choose the most appropriate answer from the options given below :

A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is :

In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of $P_1$ and $P_2$ are orthogonal to each other. The polarizer $P_3$ covers both the slits with its transmission axis at $45^{\circ}$ to those of $P_1$ and $P_2$. An unpolarized light of wavelength $\lambda$ and intensity $I_0$ is incident on $P_1$ and $P_2$. The intensity at a point after $P_3$ where the path difference between the light waves from $s_1$ and $s_2$ is $\frac{\lambda}{3}$, is 

The Young's double slit interference experiment is performed using light consisting of 480 nm and 600 nm wavelengths to form interference patterns. The least number of the bright fringes of 480 nm light that are required for the first coincidence with the bright fringes formed by 600 nm light is

Two polarisers $P_1$ and $P_2$ are placed in such a way that the intensity of the transmitted light will be zero. A third polariser $P_3$ is inserted in between $P_1$ and $\mathrm{P}_2$, at the particular angle between $\mathrm{P}_2$ and $\mathrm{P}_3$. The transmitted intensity of the light passing the through all three polarisers is maximum. The angle between the polarisers $\mathrm{P}_2$ and $\mathrm{P}_3$ is :

A monochromatic light of frequency $5 \times 10^{14} \mathrm{~Hz}$ travelling through air, is incident on a medium of refractive index ' 2 '. Wavelength of the refracted light will be :

Two light beams fall on a transparent material block at point 1 and 2 with angle \(\theta_1\) and \(\theta_{2^{\prime}}\) respectively, as shown in figure. After refraction, the beams intersect at point 3 which is exactly on the interface at other end of the block. Given : the distance between 1 and 2, \(\mathrm{d}=4 \sqrt{3} \mathrm{~cm}\) and \(\theta_1=\theta_2=\cos ^{-1}\left(\frac{\mathrm{n}_2}{2 \mathrm{n}_1}\right)\), where refractive index of the block \(\mathrm{n}_2\gt\) refractive index of the outside medium \(\mathrm{n}_1\), then the thickness of the block is ________ cm. 

In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex refractive meniscus towards $A$. If an object placed at 13 cm from the vertex of the meniscus in A forms an image with a magnification of ' $-2^{\prime}$ then the radius of curvature of meniscus is :

A concave mirror of focal length $f$ in air is dipped in a liquid of refractive index $\mu$. Its focal length in the liquid will be: