Question

One plano-convex and one plano-concave lens of the same radius of curvature $R$ but of different materials are joined side by side as shown in the figure. If the refractive index of the material of $1$ is ${\mathrm{\mu }}_1$ and that of $2$ is${\mathrm{ }\mathrm{\mu }}_2$, then the focal length of the combination is:

JEE Main 2019 (10 Apr Shift 1)

Options

• A: $\frac{R}{2-\left({\mathrm{\mu }}_1-{\mathrm{\mu }}_2\right)}$
• B: $\frac{R}{2\left({\mathrm{\mu }}_1-{\mathrm{\mu }}_2\right)}$
• C: $\frac{2R}{{\mathrm{\mu }}_1-{\mathrm{\mu }}_2}$
• D: $\frac{R}{{\mathrm{\mu }}_1-{\mathrm{\mu }}_2}$

Question

For a concave lens of focal length $f$, the relation between object and image distance $u$ and $v,$ respectively, from its pole can best be represented by ($u=v$ is the reference line):

JEE Main 2020 (05 Sep Shift 1)

Options

• A:
• B:
• C:
• D:

Question

A vessel of depth $2\mathrm{h}$ is half filled with a liquid of refractive index $2\sqrt{2}$ and the upper half with another liquid of refractive index $\sqrt{2}$ . The liquids are immiscible. The apparent depth of the inner surface of the bottom of the vessel will be

JEE Main 2020 (09 Jan Shift 1)

Options

• A: $\frac{\mathrm{h}}{\sqrt{2}}$
• B: $\frac{\mathrm{h}}{2\left(\sqrt{2}+1\right)}$
• C: $\frac{\mathrm{h}}{3\sqrt{2}}$
• D: $\frac{3\sqrt{2}\mathrm{h}}{4}$

Question

An observer can see through a small hole on the side of a jar (radius $15 \mathrm{cm}$ ) at a point at height of $15 \mathrm{cm}$ from the bottom (see figure). The hole is at a height of $45 \mathrm{cm}$. When the jar is filled with a liquid up to a height of $30 \mathrm{cm}$ the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid is$\frac{\mathrm{N}}{100},$ where $\mathrm{N}$ is an integer, the value of $\mathrm{N}$ is

JEE Main 2020 (03 Sep Shift 1)

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Question

A thin lens made of glass (refractive index $=1.5$ ) of focal length $f=16\mathrm{}\mathrm{c}\mathrm{m}$ is immersed in a liquid of refractive index $1.42$ . If its focal length in liquid is $f_l$ , then the ratio $f_l/f$ is closest to the integer:

JEE Main 2020 (07 Jan Shift 2)

Options

• A: $1$
• B: $9$
• C: $5$
• D: $17$

Question

An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror. The graphical representation of the magnitude of linear magnification $\left(\mathrm{m}\right)$ versus distance of the object from the mirror $\left(\mathrm{x}\right)$ is correctly given by
(Graphs are drawn schematically and are not to scale)

JEE Main 2020 (08 Jan Shift 2)

Options

• A:
• B:
• C:
• D:

Question

There is a small source of light at some depth below the surface of water (refractive index $=\frac{4}{3}$ ) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly):
[Use the fact that surface area of a spherical cap of height $h$ and radius of curvature $r$ is $2\pi rh$ ]

JEE Main 2020 (09 Jan Shift 2)

Options

• A: $21\%$
• B: $34\%$
• C: $17\%$
• D: $50\%$

Question

The angle of deviation through a prism is minimum when 

(A) Incident ray and emergent ray are symmetric to the prism

(B) The refracted ray inside the prism becomes parallel to its base

(C) Angle of incidence is equal to that of the angle of emergence

(D) When angle of emergence is double the angle of incidence

Choose the correct answer from the options given below :

JEE Main 2021 (16 Mar Shift 1)

Options

• A: Statements (A),(B) and (C) are true
• B: Only statement (D) is true
• C: Only statements (A) and (B) are true
• D: Statements (B) and (C) are true

Question

Your friend is having eye sight problem. She is not able to see clearly a distant uniform window mesh and it appears to her as nonuniform and distorted. The doctor diagnosed the problem as :

JEE Main 2021 (18 Mar Shift 1)

Options

• A: Astigmatism
• B: Myopia with Astigmatism
• C: Presbyopia with Astigmatism
• D: Myopia and hypermetropia

Question

The incident ray, reflected ray and the outward drawn normal are denoted by the unitvectors $\overrightarrow{a},\overrightarrow{b}$and $\overrightarrow{c}$ respectively. Then choose the correct relation for these vectors.

JEE Main 2021 (26 Feb Shift 2)

Options

• A: $\overrightarrow{b}=\overrightarrow{a}+2\overrightarrow{c}$
• B: $\overrightarrow{b}=2\overrightarrow{a}+\overrightarrow{c}$
• C:

  $\overrightarrow{b}=\overrightarrow{a}-2\left(\overrightarrow{a}·\overrightarrow{c}\right)\overrightarrow{c}$

• D: $\overrightarrow{b}=\overrightarrow{a}-\overrightarrow{c}$

Question

Find the distance of the image from object $O,$ formed by the combination of lenses in the figure:

JEE Main 2021 (27 Aug Shift 1)

Options

• A: $75 \mathrm{cm}$
• B: $10 \mathrm{cm}$
• C: infinity
• D: $20 \mathrm{cm}$

Question

Two plane mirrors $M_1$ and $M_2$ are at right angle to each other shown. A point source $P$ is placed at $a$ and $2a$ meter away from $M_1$ and $M_2$ respectively. The shortest distance between the images thus formed is : (Take $\sqrt{5}=2.3$)

JEE Main 2021 (31 Aug Shift 1)

Options

• A: $2.3 a$
• B: $2\sqrt{10}a$
• C: $4.6a$
• D: $3a$

Question

The image of an object placed in air formed by a convex refracting surface is at a distance of $10 \mathrm{m}$ behind the surface. The image is real and is at $\frac{2^{rd}}{3}$ of the distance of the object from the surface. The wavelength of light inside the surface is $\frac{2}{3}$ times the wavelength in air. The radius of the curved surface is $\frac{x}{13} \mathrm{m}$, the value of $x$ is ______ .

JEE Main 2021 (17 Mar Shift 2)

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Question

An object is placed at a distance of $12 \mathrm{cm}$ from a convex lens. A convex mirror of focal length $15 \mathrm{cm}$ is placed on another side of the lens at $8 \mathrm{cm}$ as shown in the figure. The image of the object coincides with the object.

When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be $\_\_\_ \mathrm{cm}$

JEE Main 2021 (26 Aug Shift 2)

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Question

Time taken by light to travel in two different materials $A$ and $B$ of refractive indices ${\mu }_A$ and ${\mu }_B$ of same thickness is $t_1$ and $t_2$ respectively. If $t_2-t_1=5\times {10}^{-10}\mathrm{s}$ and the ratio of ${\mu }_A$ to ${\mu }_B$ is $1:2$. Then the thickness of material, in meter is: (Given $v_A$ and $v_B$ are velocities of light in $A$ and $B$ materials respectively).

JEE Main 2022 (25 Jul Shift 1)

Options

• A: $5\times {10}^{-10}{v}_A \mathrm{m}$
• B: $5\times {10}^{-10} \mathrm{m}$
• C: $1.5\times {10}^{10} \mathrm{m}$
• D: $5\times {10}^{-10}{v}_B \mathrm{m}$

Question

A convex lens has power $P$. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figures). Choose the incorrect option for the reported pieces.

JEE Main 2022 (27 Jun Shift 2)

Options

• A: Power of $L_1=\frac{P}{2}$
• B: Power of $L_2=\frac{P}{2}$
• C: Power of $L_3=\frac{P}{2}$
• D: Power of $L_1=P$

Question

In the given figure, the face $AC$ of the equilateral prism is immersed in a liquid of refractive index $n$. For incident angle $60°$ at the side $AC$, the refracted light beam just grazes along face $AC$. The refractive index of the liquid $n=\frac{\sqrt{x}}{4}$. The value of $x$ is _____ .
(Given refractive index of glass $=1.5$)

JEE Main 2022 (26 Jul Shift 2)

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Question

A light ray is incident, at an incident angle ${\theta }_1$, on the system of two plane mirrors $M_1$ and $M_2$ having an inclination angle $75°$ between them (as shown in figure). After reflecting from mirror $M_1$ it gets reflected back by the mirror $M_2$ with an angle of reflection $30°$. The total deviation of the ray will be _____ degree.

JEE Main 2022 (26 Jun Shift 1)

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Question

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 $1 \mathrm{m}$ 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:

JEE Main 2023 (06 Apr Shift 2)

Options

• A: $0.85$
• B: $1.70$
• C: $1.02$
• D: $0.51$

Question

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 

JEE Main 2023 (12 Apr Shift 1)

Options

• A: $\frac{3}{2}$
• B: $\frac{2}{3}$
• C: $\frac{6}{5}$
• D: $\frac{4}{3}$

Question

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 $\mathrm{x}=$ ______ $\mathrm{cm}$, from concave lens.

JEE Main 2023 (24 Jan Shift 1)

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Question

A light ray is incident on a glass slab of thickness $4 \sqrt{3} \mathrm{~cm}$ and refractive index $\sqrt{2}$ . The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is _____ $\mathrm{cm}$. $\left(\right.$ Given $\left.\sin 15^{\circ}=0.25\right)$

JEE Main 2024 (04 Apr Shift 2)

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Question

The refractive index of prism is $\mu=\sqrt{3}$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _______.

JEE Main 2024 (06 Apr Shift 1)

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Question

In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division $=49 \mathrm{MSD} ; 20$ divisions on main scale in each $\mathrm{cm}$ For mark on paper $\mathrm{MSR}=8.45 \mathrm{~cm}, \mathrm{VC}=26$ For mark on paper seen through slab MSR $=7.12 \mathrm{~cm}, V C=41$ For powder particle on the top surface of the glass slab $\mathrm{MSR}=4.05 \mathrm{~cm}, \mathrm{VC}=1$ (MSR $=$ Main Scale Reading, VC $=$ Vernier Coincidence) Refractive index of the glass slab is :

JEE Main 2024 (06 Apr Shift 2)

Options

• A: 1.52
• B: 1.35
• C: 1.42
• D: 1.24

Question

The position of the image formed by the combination of lenses is :

JEE Main 2024 (08 Apr Shift 2)

Options

• A: $15 \mathrm{~cm}$ (right of second lens)
• B: $30 \mathrm{~cm}$ (left of third lens)
• C: $15 \mathrm{~cm}$ (left of second lens)
• D: $30 \mathrm{~cm}$ (right of third lens)