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Refer the figure given below, \( \mu_{1} \) and \( \mu_{2} \) are refractive indices of air and lens material. The height of image will be ____ \( \text{cm} \).

An unpolarized 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 ______.

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 \( 40 \, \text{cm} \). The focal length of the mirror used is _______________ cm.

A rod of length \( 10 \, \text{cm} \) lies along the principle axis of a concave mirror of focal length \( 10 \, \text{cm} \) as shown in figure. The length of the image is ______ \( \text{cm} \).

As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface.

If refractive index of the material of prism is \( \sqrt{2} \), the angle \( \theta \) of prism is.

A parallel beam of light travelling in air (refractive index \(1.0\)) is incident on a convex spherical glass surface of radius of curvature \(50 \, \text{cm}\). Refractive index of glass is \(1.5\). The rays converge to a point at a distance \( x \, \text{cm} \) from the centre of the curvature of the spherical surface. The value of \( x \) is __________ \( \text{cm} \).

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

A convex lens is made from glass material having refractive index of \( 1.4 \) with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is __________.

If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at \( 30\ \text{cm} \) above the paper. If the radius of curvature of the lens is \( 60\ \text{cm} \) then the refractive index of the lens material is \( \frac{\alpha}{10} \). The value of \( \alpha \) is __________.

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

Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media A and B are \( 2.4 \times 10^8 \, \text{m/s} \) and \( 2.7 \times 10^8 \, \text{m/s} \), respectively, then the value of critical angle is:

Consider an equilateral prism (refractive index $\sqrt{2}$). A ray of light is incident on its one surface at a certain angle $i$. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to _________.

A ray light passing through an equilateral prism is having velocity \( 2.12 \times 10^{8} \, \text{m/s} \) in the prism material, then the minimum angle of deviation is ______ degrees.

A thin prism with angle \( 5^\circ \) of refractive index \( 1.72 \) is combined with another prism of refractive index \( 1.9 \) to produce dispersion without deviation. The angle of second prism is ______.

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 plano-concave 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 convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses?

In parallax method for the determination of focal length of a concave mirror, the object should always be placed:

A thin biconvex lens is prepared from the glass \( (\mu=1.5) \) both curved surfaces of which have equal radii of \( 20 \,\text{cm} \) 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 ______ \( \text{cm} \).

A prism of angle \( 75^\circ \) and refractive index \( \sqrt{3} \) is coated with thin film of refractive index \( 1.5 \) only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be ______.
\( (\sin 15^\circ = 0.25 \text{ and } \sin 25^\circ = 0.43) \)

One side of an equilateral prism is painted by a transparent material of refractive index \( n_{2} \). The refractive index of prism is \( 1.6 \). The minimum value of \( n_{2} \) required for total internal reflection from painted face is ______.

A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnification keeping the object distance unchanged, the tube length has to be

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

A convex lens of refractive index \( 1.5 \) and focal length \( f = 18 \, \text{cm} \) is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is \( \alpha \times f \). The value of \( \alpha \) is __________. (refractive index of water \( = \frac{4}{3} \))

The wavelength of light, while it is passing through water is \( 540 \,\text{nm} \). The refractive index of water is \( \frac{4}{3} \). The wavelength of the same light when it is passing through a transparent medium having refractive index of \( \frac{3}{2} \) is ________ \( \text{nm} \).

$7.9\text{ MeV}$ $\alpha$-particle scatters from a target material of atomic number $79$. From the given data the estimated diameter of nuclei of the target material is (approximately) _________ $\text{m}$.
$\left[ \frac{1}{4\pi\epsilon_0} = 9 \times 10^9\text{ Nm}^2/\text{C}^2 \text{ and electron charge} = 1.6 \times 10^{-19}\text{ C} \right]$

A thin convex lens of focal length \( 5 \, \text{cm} \) and a thin concave lens of focal length \( 4 \, \text{cm} \) are combined together (without any gap) and this combination has magnification \( m_1 \) when an object is placed \( 10 \, \text{cm} \) before the convex lens. Keeping the positions of convex lens and object undisturbed a gap of \( 1 \, \text{cm} \) is introduced between the lenses by moving the concave lens away, which lead to a change in magnification of total lens system to \( m_2 \). The value of \( \left| \dfrac{m_1}{m_2} \right| \) is ________.

The size of the image of an object, formed by a thin lens are equal when the object is placed at two different positions \( 8 \; \mathrm{cm} \) and \( 24 \; \mathrm{cm} \) from the lens. The focal length of the lens is ______ \( \mathrm{cm} \).

Light ray incident along a vector \( \overrightarrow{AO} \, ( \overrightarrow{AO} = 2\hat{i} - 3\hat{j} ) \) emerges out along vector \( \overrightarrow{OB} \, ( \overrightarrow{OB} = C\hat{i} - 4\hat{j} ) \) as shown in the figure below. The value of \( C \) is _______.

A collimated beam of light of diameter \( 2 \, \text{mm} \) is propagating along \( x \)-axis. The beam is required to be expanded in a collimated beam of diameter \( 14 \, \text{mm} \) using a system of two convex lenses. If first lens has focal length \( 40 \, \text{mm} \), then the focal length of second lens is __________ \( \text{mm} \).

In a microscope of tube length \( 10 \, \text{cm} \) two convex lenses are arranged with focal length of \( 2 \, \text{cm} \) and \( 5 \, \text{cm} \). Total magnification obtained with this system for normal adjustment is \( (5)^k \). The value of \( k \) is ______.

A concave mirror of focal length \( 10 \, \text{cm} \) forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is ______ \( \text{cm} \).

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JEE Main 2026 23rd Jan Morning Shift

A thin prism with angle \( 5^\circ \) of refractive index \( 1.72 \) is combined with another prism of refractive index \( 1.9 \) to produce dispersion without deviation. The angle of second prism is ______.