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JEE Mains | PYQ

An object viewed from a near point distance of \( 25 \, \text{cm} \), 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 of length \( 0.6 \, \text{m} \), if the focal length of the eyepiece is equal to __________ \( \text{cm} \).

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 non-uniform and distorted. The doctor diagnosed the problem as:

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

The thickness at the centre of a plano convex lens is \( 3 \, \text{mm} \) and the diameter is \( 6 \, \text{cm} \). If the speed of light in the material of the lens is \( 2 \times 10^{8} \, \text{m s}^{-1} \). The focal length of the lens is __________.

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

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:

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 \( r' \). The critical angle is given by:

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?

Curved surfaces of a plano-convex lens of refractive index \( \mu_1 \) and a plano-concave 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.

A ray of light entering from air into a denser medium of refractive index \( \dfrac{4}{3} \) 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:

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

A ray of light passing through a prism \( (\mu = \sqrt{3} )\) suffers 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).

Cross-section view of a prism is the equilateral triangle \( ABC \) shown 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 _______ \( \times 10^{-10} \, \text{s} \). (Given, speed of light in vacuum \( = 3 \times 10^{8} \, \text{m/s} \) and \( \cos 30^{\circ} = \frac{\sqrt{3}}{2} \))

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 \( \sqrt{5} = 2.3 \).)

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 \( \dfrac{2^{rd}}{3} \) of the distance of the object from the surface. The wavelength of light inside the surface is \( \dfrac{2}{3} \) times the wavelength in air. The radius of the curved surface is \( \dfrac{x}{13}\,m \). The value of 'x' is ________.

The refractive index of a converging lens is \( 1.4 \). What will be the focal length of this lens 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 ray of laser of a wavelength \( 630 \ \text{nm} \) is incident at an angle of \( 30^\circ \) at the diamond–air interface. It is going from diamond to air. The refractive index of diamond is \( 2.42 \) and that of air is \( 1 \). Choose the correct option.