Geometrical Optics — JEE Main PYQs

A light wave travelling linearly in a medium of dielectric constant 4, incident on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be (Given: relative perme …

The difference of speed of light in the two media $A$ and $B$ $(v_A-v_B)$ is $2.6\times 10^{7}m/s$. If the refractive index of medium $B$ is 1.47, then the ratio of refractive index of medium $B$ to medium $A$ is: (Given: speed of light in vacuum …

Car B overtakes another car A at a relative speed of $40{\mathrm{ms}}^{-1}$. How fast will the image of car B appear to move in the mirror of focal length 10 cm fitted in car $A$, when the car $B$ is 1.9 m away from the car A ?

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

An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on other side of lens at 8 cm as shown in the figure. Image of object coincides with the object. When the convex mirror is removed, a real and inverted image is formed a …

Region I and II are separated by a spherical surface of radius 25 cm. An object is kept in region I at a distance of 40 cm from the surface. The distance of the image from the surface is :

An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification '6', gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube …

Curved surfaces of a plano-convex lens of refractive index ${\mu }_1$ and a planoconcave lens of refractive index ${\mu }_2$ have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.

The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of convex lens is ____ cm.

A ray of light passes from a denser medium to a rarer medium at an angle of incidence i. The reflected and refracted rays make an angle of $90^{\circ }$ with each other. The angle of reflection and refraction are respectively $r$ and $r^{\prime }$. The critical angle is given by :

A ray of light passing through a prism $(\mu =\sqrt{3})$ surface minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is ______ (in degrees).

A short straight object of height 100 cm lies before the central axis of a spherical mirror whose focal length has absolute value $|\mathrm{f}|=40\mathrm{cm}$. The image of object produced by the mirror is of height 25 cm and has the same orientation of the object. One may co …

An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is $d_1$ from C and the distance of the image formed is $d_2$ from C, the radius of curvature of this mirror is :

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

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

Given below are two statements: one is labeled as Assertion A and the other is labeled as Reason R.
Assertion A: For a simple microscope, the angular size of the object equals the angular size of the image.
Reason R: Magnification is achieved as the small object can be kept much …

A point source of light S , placed at a distance 60 cm infront of the centre of a plane mirror of width 50 cm , hangs vertically on a wall. A man walks infront of the mirror along a line parallel to the mirror at a distance 1.2 m from it (see in the figure). The distance between …

Cross-section view of a prism is the equilateral triangle $ABC$ in the figure. The minimum deviation is observed using this prism when the angle of incidence is equal to the prism angle. The time taken by light to travel from P (midpoint of BC) to A is ______ …

Two plane mirrors ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ are at right angle to each shown. A point source ' P ' is placed at ' a ' and ' 2 a ' meter away from $M_1$ and $M_2$ respectively. The shortest distance between the images thus formed is : (Take $\sqrt{5}=2.3$ …

An object is placed at the focus of concave lens having focal length f . What is the magnification and distance of the image from the optical centre of the lens?

A prism of refractive index ${\mathrm{n}}_1$ and another prism of refractive index ${\mathrm{n}}_2$ are stuck together (as shown in the figure). ${\mathrm{n}}_1$ and ${\mathrm{n}}_2$ depend on $\lambda$, the wavelength of light, according to the relation …

The thickness at the centre of a plano-convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is $2\times 10^8{\mathrm{ms}}^{-1}$. The focal length of the lens is:

A ray of laser of a wavelength 630 nm is incident at an angle of $30^{\circ }$ at the diamond-air interface. It is going from diamond to air. The refractive index diamond is 2.42 and that of air is 1. Choose the correct option.

A ray of light entering from air into a denser medium of refractive index $\frac{4}{3}$, as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle $\theta$ should be equal to :

A prism of refractive index $\mu$ and angle of prism $A$ is placed in the position of minimum angle of deviation. If minimum angle of deviation is also $A$, then in terms of refractive index value of $A$ is :

The expected graphical representation of the variation of angle of deviation '$\delta$' with angle of incidence '$i$' in a prism is :

A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water ($\mu =4/3$) into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actu …

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 if incidence is equal to that of the angle of emergence
(D) When angle of emergence is …

The refractive index of converging lens is 1.4 . What will be the focal length of this if it is placed in a medium of same refractive index? Assume the radii of curvature of the faces of lens are $R_1$ and $R_2$ respectively.

A deviation of $2^0$ is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass as 0.02 and 0.03 respectively and refractive index for yellow light for these glasses are 1.5 and 1.6 respective …

Three rays of light, red ( R ), green( G) and blue ( B) are incident on the face PQ of a right angled prism PQR as shown in the figure.
The refractive indices of material of the prism for red , green and blue wavelength are 1.27, 1.42 and 1.49 respectively. The colour of ray(s) e …

The image of an object placed in air formed by a convex refracting surface is at a distance of 10 m behind the surface. The image is real and is at $\frac{2^{\text{rd}}}{3}$ of the distance of the object from the surface. The wavelength of light inside the surface is …

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

If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5 mm, the focal length of the eye piece should be close to

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

The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability $\frac{4}{3}$ for this wavelength, will be

The magnifying power of a telescope with tube length 60 cm is 5 . What is the focal length of its eye piece?

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is 30 cm and the refractive index of the lens material is 1.5, then the focal length of the lens (in cm ) is ____ .

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 (m) versus distance of the object from the mirror (x) is correctly given by (Graphs are drawn schematica …

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 (n …

A vessel of depth $2h$ 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 vessel will be

A prism of angle $\mathrm{A}=1^{\circ }$ has a refractive index $\mu =1.5$. A good estimate for the minimum angle of deviation (in degrees) is close to N/10. Value of N is ____.

An observer can see through a small hole on the side of a jar (radius 15 cm) at a point at height of 15 cm from the bottom (see figure). The hole is at a height of 45 cm. When the jar is filled with a liquid up to a height of 30 cm the same observer can see the edge at the bottom …

When an object is kept at a distance of 30 cm from a concave mirror, the image is formed at a distance of 10 cm from the mirror. If the object is moved with a speed of 9 ${\mathrm{cm}\mathrm{s}}^{-1}$, the speed (in ${\mathrm{cm}\mathrm{s}}^{-1}$) with which image moves at that instant is ______.

A double convex lens has power $P$ and same radii of curvature $R$ of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power 1.5 P is

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

A compound microscope consists of an objective lens of focal length 1 cm and an eye piece of focal length 5 cm with a separation of 10 cm. The distance between an object and the objective lens, at which the strain on the eye is minimum is $\frac{n}{40}$ cm. The value of n is ____ …

A point like object is placed at a distance of 1 m in front of convex lens of focal length 0.5 m. A plane mirror is placed at a distance of 2 m behind the lens. The position and nature of the final image formed by the system is:

In a compound microscope, the magnified virtual image is formed at a distance of 25 cm from the eye-piece. The focal length of its objective lens is 1 cm. If the magnification is 100 and the tube length of the microscope is 20 cm, then the focal length of the eyepiece lens (in cm …

The distance between an object and a screen is 100 cm. A lens can produce real image of the object on the screen for two different positions between the screen and the object.

The distance between these two positions is 40 cm. If the power of the lens is close to …