JEE Main 2023 — Optics

An object is placed at a distance of $12\mathrm{cm}$ in front of a plane mirror. The virtual and erect image is formed by the mirror. Now the mirror is moved by $4\mathrm{cm}$ towards the stationary object. The distance by which the position of image would be shifted, will be

In a single slit diffraction pattern the angular width of the central maximum is 0.1 rad...

Two convex lenses of focal length $20\mathrm{cm}$ each are placed coaxially with a separation of $60\mathrm{cm}$ between them. The image of the distant object formed by the combination is at _____ $\mathrm{cm}$ from the first lens.

An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is $12\mathrm{cm}$. When viewed from the opposite side, the apparent distance of the bubble is observed as $4\mathrm{cm}$. If the side of the ice cube is $24\mathrm{cm}$, the refractive index of the ice cube is

The critical angle for a denser-rarer interface is $45^{\circ}$. The speed of light in rarer medium is $3\times {10}^{8}m{s}^{-1}$. The speed of light in the denser medium is:

Two transparent media having refractive indices $1.0$ and $1.5$ are separated by a spherical refracting surface of radius of curvature $30\mathrm{cm}$. The centre of curvature of surface is towards denser medium and a point object is placed on the principal axis in rarer medium at a distance of $15\mathrm{cm}$ from the pole of the surface. The distance of image from the pole of the surface is $\mathrm{cm}$.

In a reflecting telescope, a secondary mirror is used to:

A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index $\frac{5}{3}$ is poured inside the bucket, then microscope have to be raised by $30\mathrm{cm}$ to focus the object again. The height of the liquid in the bucket is :

In a medium the speed of light wave decreases to $0.2$ times to its speed in free space. The ratio of relative permittivity to the refractive index of the medium is $x:1$. The value of $x$ is ______. (Given speed of light in free space $=3\times {10}^{8}m{s}^{-1}$ and for the given medium ${\mu }_{r}=1$)

A thin prism ${P}_{1}$ with an angle $6^{\circ}$ and made of glass of refractive index $1.54$ is combined with another prism ${P}_{2}$ made from glass of refractive index $1.72$ to produce dispersion without average deviation. The angle of prism ${P}_{2}$ is :

When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called :

An object is placed on the principal axis of convex lens of focal length $10\mathrm{cm}$ as shown. A plane mirror is placed on the other side of lens at a distance of $20\mathrm{cm}$. The image produced by the plane mirror is $5\mathrm{cm}$ inside the mirror. The distance of the object from the lens is ____ $\mathrm{cm}$. 

A single slit of width $a$ is illuminated by a monochromatic light of wavelength $600\mathrm{nm}$. The value of $a$ for which first minimum appears at $\theta ={30}^{o}$ on the screen will be :

The width of fringe is $2\mathrm{mm}$ on the screen in a double slit experiment for the light of wavelength of $400\mathrm{nm}$. The width of the fringe for the light of wavelength $600\mathrm{nm}$ will be:

Two light waves of wavelengths $800$ and $600\mathrm{nm}$ are used in Young's double slit experiment to obtain interference fringes on a screen placed $7m$ away from plane of slits. If the two slits are separated by $0.35\mathrm{mm}$, then shortest distance from the central bright maximum to the point where the bright fringes of the two wavelength coincide will be ______ $\mathrm{mm}$.

A beam of light consisting of two wavelengths $7000\overset{o}{A}$ and $5500\overset{o}{A}$ is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is $2.5\mathrm{mm}$ and the distance between the plane of slits and the screen is $150\mathrm{cm}$. The least distance from the central fringe, where the bright fringes due to both the wavelengths coincide, is $n\times {10}^{–5}m$. The value of $n$ is _____.

Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are $2.8$ (medium –$1$) and $6.8$ (medium – $2$), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be ${\mathrm{tan}}^{-1}{(1+\frac{10}{\theta })}^{\frac{1}{2}}$, the value of $\theta$ is ______. (Given for dielectric media, ${\mu }_{r}=1$)

Given below are two statements : Statement I : If the Brewster's angle for the light propagating from air to glass is ${\theta }_{B}$, then Brewster's angle for the light propagating from glass to air is $\frac{\pi }{2}-{\theta }_{B}$. Statement II : The Brewster's angle for the light propagating from glass to air is ${\mathrm{tan}}^{-1}({\mu }_{g})$, where ${\mu }_{g}$ is the refractive index of glass. In the light of the above statements, choose the correct answer from the options given below :

In Young's double slits experiment, the position of 5$^{th}$ bright fringe from the central maximum is $5\mathrm{cm}$. The distance between slits and screen is $1m$ and wavelength of used monochromatic light is $600\mathrm{nm}$. The separation between the slits is:

In a Young’s double slit experiment, the ratio of amplitude of light coming from slits is $2:1$. The ratio of the maximum to minimum intensity in the interference pattern is

In a Young’s double slit experiment, the intensities at two points, for the path difference $\frac{\lambda }{4}$ and $\frac{\lambda }{3}$ ($\lambda$ being the wavelength of light used) are ${I}_{1}$ and ${I}_{2}$ respectively. If ${I}_{0}$ denotes the intensity produced by each one of the individual slits, then $\frac{{I}_{1}+{I}_{2}}{{I}_{0}}=______$.

A fish rising vertically upward with a uniform velocity of $8m{s}^{–1},$ observes that a bird is diving vertically downward towards the fish with the velocity of $12m{s}^{–1}.$ If the refractive index of water is $\frac{4}{3},$ then the actual velocity of the diving bird to pick the fish, will be$__________m{s}^{-1}.$ 

A person has been using spectacles of power $-1.0$ diopter for distant vision and a separate reading glass of power $2.0$ diopters. What is the least distance of distinct vision for this person:

A vessel of depth $d$ is half filled with oil of refractive index ${n}_{1}$ and the other half is filled with water of refractive index ${n}_{2}.$ The apparent depth of this vessel when viewed from above will be-

A ray of light is incident from air on a glass plate having thickness $\sqrt{3}\mathrm{cm}$ and refractive index $\sqrt{2}$. The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is $____\times {{10}^{-}}^{2}\mathrm{cm}$ . (given $\mathrm{sin}15^{\circ}=0.26$)

Two objects $AandB$ are placed at $15\mathrm{cm}\mathrm{and}25\mathrm{cm}$ from the pole in front of a concave mirror having radius of curvature $40\mathrm{cm}$. The distance between images formed by the mirror is:

As shown in the figure, a combination of a thin plano-concave lens and a thin plano-convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is $30\mathrm{cm}$ and refraction index of the material for both the lenses is $1.75$. Both the lenses are placed at distance of $40\mathrm{cm}$ from each other. Due to the combination, the image of the object is formed at distance $x=$ ______ $\mathrm{cm}$, from concave lens. 

In an experiment for estimating the value of focal length of converging mirror, image of an object placed at $40\mathrm{cm}$ from the pole of the mirror is formed at distance $120\mathrm{cm}$ from the pole of the mirror. These distances are measured with a modified scale in which there are $20$ small divisions in $1\mathrm{cm}$. The value of error in measurement of focal length of the mirror is $\frac{1}{K}\mathrm{cm}$. The value of $K$ is ______.

As shown in figures, three identical polaroids ${P}_{1}$, ${P}_{2}$ and ${P}_{3}$ are placed one after another. The pass axis of ${P}_{2}$ and ${P}_{3}$ are inclined at angle of $60º$ and $90º$ with respect to axis of ${P}_{1}$. The source $S$ has an intensity of $256W{m}^{-2}$. The intensity of light at point $O$ is _____$W{m}^{-2}$. 

As shown in the figure, in Young's double slit experiment, a thin plate of thickness $t=10\mu m$ and refractive index $\mu =1.2$ is inserted infront of slit ${S}_{1}$. The experiment is conducted in air ($\mu =1$) and uses a monochromatic light of wavelength $\lambda =500\mathrm{nm}$. Due to the insertion of the plate, central maxima is shifted by a distance of $x{\beta }_{0}$. ${\beta }_{0}$ is the fringe-width before the insertion of the plate. The value of the $x$ is ______. 

In Young’s double slit experiment, two slits ${S}_{1}$ and ${S}_{2}$ are $d$ distance apart and the separation from slits to screen is $D$ (as shown in figure). Now if two transparent slabs of equal thickness $0.1\mathrm{mm}$ but refractive index $1.51$ and $1.55$ are introduced in the path of beam $(\lambda =4000Å)$ from ${S}_{1}$ and ${S}_{2}$ respectively. The central bright fringe spot will shift by ________ number of fringes. 

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: The phase difference of two light waves change if they travel through different media having same thickness, but different indices of refraction. Reason R: The wavelengths of waves are different in different media. In the light of the above statements, choose the most appropriate answer from the options given below

A pole is vertically submerged in swimming pool, such that it gives a length of shadow $2.15m$ within water when sunlight is incident at an angle of $30^{\circ}$ with the surface of water. If swimming pool is filled to a height of $1.5m,$ then the height of the pole above the water surface in centimeters is $({n}_{w}=\frac{4}{3})________.$

The refractive index of a transparent liquid filled in an equilateral hollow prism is $\sqrt{2}$. The angle of minimum deviation for the liquid will be _______$^{\circ}$.

As shown in the figure, a plane mirror is fixed at a height of $50\mathrm{cm}$ from the bottom of tank containing water $(\mu =\frac{4}{3})$. The height of water in the tank is $8\mathrm{cm}$. A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed by mirror from the bottom of the tank is ______ $\mathrm{cm}$. 

The ratio of intensities at two points $P$ and $Q$ on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are $\frac{\pi }{3}$ and $\frac{\pi }{2}$, respectively are

A thin cylindrical rod of length $10\mathrm{cm}$ is placed horizontally on the principle axis of a concave mirror of focal length $20\mathrm{cm}$. The rod is placed in a such a way that mid point of the rod is at $40\mathrm{cm}$ from the pole of mirror. The length of the image formed by the mirror will be $\frac{x}{3}\mathrm{cm}$. The value of $x$ is ______.

‘$n$’ polarizing sheets are arranged such that each makes an angle $45^{\circ}$ with the proceeding sheet. An unpolarized light of intensity $I$ is incident into this arrangement. The output intensity is found to be $\frac{I}{64}$ . The value of $n$ will be:

A $2$ meter long scale with least count of $0.2\mathrm{cm}$ is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at $80\mathrm{cm}$ mark and $1m$ mark, respectively. The image of the object pin on the other side of lens coincides with image pin that is kept at $180\mathrm{cm}$ mark. The $%$ error in the estimation of focal length is:

A bi convex lens of focal length $10\mathrm{cm}$ is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is _____ $D$.

When one light ray is reflected from a plane mirror with $30^{\circ}$ angle of reflection, the angle of deviation of the ray after reflection is:

Unpolarised light of intensity $32W{m}^{-2}$ passes through the combination of three polaroids such that the pass axis of the last polaroids is perpendicular to that of the pass axis of first polaroids. If intensity of emerging light is $3W{m}^{-2}$, then the angle between pass axis of first two polaroids is _________$^{\circ}$.

Two vertical parallel mirrors $A$ and $B$ are separated by $10$ cm. $A$ point object $O$ is placed at a distance of $2\mathrm{cm}$ from mirror $A.$ The distance of the second nearest image behind mirror $A$ from the mirror $A$ is $_______\mathrm{cm}.$ 

Two polaroids $A\text{and}B$ are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid $C$ is placed between $A\text{and}B$ bisecting angle between them. If intensity of unpolarised light is ${I}_{0}$ then intensity of transmitted light after passing through polaroid $B$ will be :

A monochromatic light wave with wavelength ${\lambda }_{1}$ and frequency ${\nu }_{1}$ in air enters another medium. If the angle of incidence and angle of refraction at the interface are $45^{\circ}$ and $30^{\circ}$ respectively, then the wavelength ${\lambda }_{2}$ and frequency ${\nu }_{2}$ of the refracted wave are:

A point object $O$ is placed in front of two thin symmetrical coaxial convex lenses ${L}_{1}$ and ${L}_{2}$ with focal length $24\mathrm{cm}$ and $9\mathrm{cm}$ respectively. The distance between two lenses is $10\mathrm{cm}$ and the object is placed $6\mathrm{cm}$ away from lens ${L}_{1}$ as shown in the figure. The distance between the object and the image formed by the system of two lenses is _____________ $\mathrm{cm}$ 

The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are :- A. Real B. Erect C. Smaller in size than object D. Laterally inverted Choose the most appropriate answer from the options given below:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R Assertion A : The beam of electrons shows wave nature and exhibit interference and diffraction. Reason R : Davisson Germer Experimentally verified the wave nature of electrons. In the light of the above statements. Choose the most appropriate answer from the options given below :

In a Young’s double slit experiment, two slits are illuminated with a light of wavelength $800\mathrm{nm}$. The line joining ${A}_{1}P$ is perpendicular to ${A}_{1}{A}_{2}$ as shown in the figure. If the first minimum is detected at $P$, the value of slits separation $a$ will be :  The distance of screen from slits $D=5\mathrm{cm}$.

A convex lens of refractive index $1.5$ and focal length $18\mathrm{cm}$ in air is immersed in water. The change in focal length of the lens will be_____$\mathrm{cm}$. (Given refractive index of water$=\frac{4}{3}$)

The radius of curvature of each surface of a convex lens having refractive index $1.8$ is $20\mathrm{cm}$. The lens is now immersed in a liquid of refractive index $1.5$. The ratio of power of lens in air to its power in the liquid will be $x:1$. The value of $x$ is