Geometrical Optics — JEE Advanced PYQs

A double convex lens made of glass of refractive index 1.5 and radii of curvature of the curved surfaces 20 cm each is immersed in a liquid of refractive index $n_{\mathrm{L}}$. The correct plot showing the variation of the power, in the units of diopter (D), as a function of …

A beam of polychromatic light passes through a thin prism of prism angle 6°. The refractive index of the material of the prism varies with wavelength $(\lambda )$ as $n(\lambda )=\alpha \lambda +\frac{\beta }{{\lambda }^2}$, where $\alpha =3\mu {\mathrm{m}}^{-1}$ and …

Consider two isosceles prisms 1 and 2 with prism angles $A_1$ and $A_2$ and refractive indices $n_1$ and $n_2$, respectively, as shown in the figure. The faces $a_1{b}_1$ and $a_2{b}_2$ are parallel to each other and perpendicular to the mirror $M$. If …

Two identical concave mirrors each of focal length $f$ are facing each other as shown in the schematic diagram. The focal length $f$ is much larger than the size of the mirrors. A glass slab of thickness $t$ and refractive index $n_0$ is kept equidistant from the mirror …

A glass beaker has a solid, plano-convex base of refractive index 1.60, as shown in the figure. The radius of curvature of the convex surface (SPU) is 9 cm, while the planar surface (STU) acts as a mirror. This beaker is filled with a liquid of refractive index $n$ up to the le …

A light ray is incident on the surface of a sphere of refractive index $n$ at an angle of incidence ${\theta }_0$. The ray partially refracts into the sphere with angle of refraction ${\varphi }_0$ and then partly reflects from the back surface. The reflected ray then emerges ou …

Two equilateral-triangular prisms ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are kept with their sides parallel to each other, in vacuum, as shown in the figure. A light ray enters prism ${\mathrm{P}}_1$ at an angle of incidence $\theta$ such that the outgoing ray undergoes minimum de …

A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is $\delta =60^{\circ }$ (see Figure-1). The angle of minimum deviation for red light from the same prism is …

A monochromatic light wave is incident normally on a glass slab of thickness d , as shown in the figure. The refractive index of the slab increases linearly from ${\mathrm{n}}_1$ to ${\mathrm{n}}_2$ over the height h . Which of the following statement(s) is (are) true about the l …

A rod of length $2cm$ makes an angle $\frac{2\pi }{3}$ rad with the principal axis of a thin convex lens. The lens has a focal length of $10cm$ and is placed at a distance of $\frac{40}{3}cm$ from the object as shown in the figure. The height of the image is …

Three plane mirrors form an equilateral triangle with each side of length $L$. There is a small hole at a distance $l>0$ from one of the corners as shown in the figure. A ray of light is passed through the hole at an angle $\theta$ and can only come out through the same hol …

List I contains four combinations of two lenses (1 and 2) whose focal lengths (in cm) are indicated in the figures. In all cases, the object is placed $20cm$ from the first lens on the left, and the distance between the two lenses is $5cm$. List II contains the positions of …

Consider a configuration of $n$ identical units, each consisting of three layers. The first layer is a column of air of height $h=\frac{1}{3}cm$, and the second and third layers are of equal thickness $d=\frac{\sqrt{3}-1}{2}cm$, and refractive indices …

An object and a concave mirror of focal length $f=10cm$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_0=15cm{s}^{-1}$ towards the mirror with respect to a laboratory frame. The distance between the object and the mirr …

For a prism of prism angle $\theta =60^{\circ }$, the refractive indices of the left half and the right half are, respectively, $n_1$ and $n_2\left(n_2\ge n_1\right)$ as shown in the figure. The angle of incidence $i$ is chosen such that the incident light rays wi …

An extended object is placed at point O, 10 cm in front of a convex lens ${\mathrm{L}}_1$ and a concave lens ${\mathrm{L}}_2$ is placed 10 cm behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are 20 cm. The refractive index of …

A wide slab consisting of two media of refractive indices ${\mathrm{n}}_1$ and ${\mathrm{n}}_2$ is placed in air as shown in the figure. A ray of light is incident from medium ${\mathrm{n}}_1$ to ${\mathrm{n}}_2$ at an angle $\theta$, where $\sin \theta$ is slightly larger than …

A large square container with thin transparent vertical walls and filled with water (refractive index $\frac{4}{3}$) is kept on a horizontal table. A student holds a thin straight wire vertically inside the water 12 cm from one of its corners, as shown schematically in the figure …

A beaker of radius $r$ is filled with water (refractive index $\frac{4}{3}$) up to a height $H$ as shown in the figure on the left. The beaker is kept on a horizontal table rotating with angular speed $\omega$. This makes the water surface curved so that the difference in the hei …

A thin convex lens is made of two materials with refractive indices ${\mathrm{n}}_1$ and ${\mathrm{n}}_2$, as shown in figure. The radius of curvature of the left and right spherical surfaces are equal. f is the focal length of the lens when …

A planar structure of length L and width W is made of two different optical media of refractive indices ${\mathrm{n}}_1=1.5$ and ${\mathrm{n}}_2=1.44$ as shown in figure. If L >> W, a ray entering from end AB will emerge from end CD only if the total internal reflection condition …

Three glass cylinders of equal height $\mathrm{H}=30\mathrm{cm}$ and same refractive index $\mathrm{n}=1.5$ are placed on a horizontal surfaces shown in figure. Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvatur …

A monochromatic light is incident from air on a refracting surface of a prism of angle 75° and refractive index ${\mathrm{n}}_0=\sqrt{3}$. The other refracting surface of a prism is coated by a thin film of material of refractive index n as shown in figure. The light suffers to …

An optical bench has 1.5 m long scale having four equal divisions in each cm. While measuring the focal length of a convex lens, the lens is kept at 75 cm mark of the scale and the object pin is kept at 45 cm mark. The image of the object pin on the other side of the lens overlap …

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length $f$, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are n …

Sunlight of intensity $1.3kW{m}^{-2}$ is incident normally on a thin convex lens of focal length $20cm$. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in $kW{m}^{-2}$ …

For an isosceles prism of angle $A$ and refractive index $\mu$, it is found that the angle of minimum deviation ${\delta }_m=A$. Which of the following options is/are correct?

A monochromatic light is travelling in a medium of refractive index $n=1.6$. It enters a stack of glass layers from the bottom side at an angle $\theta =30^{\circ }$. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers …

A parallel beam of light is incident from air at an angle $\alpha$ on the side PQ of a right angled triangular prism of refractive index $n=\sqrt{2}$. Light undergoes total internal reflection in the prism at the face PR when $\alpha$ has a minimum value of 45°. The angle …

A plano-convex lens is made of a material of refractive index $n$. When a small object is placed 30 cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens, another faint im …

A transparent slab of thickness $d$ has a refractive index $n(z)$ that increases with $z$. Here $z$ is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices $n_1$ and $n_2(>n_1)$, as sh …

A small object is placed 50 cm to the left of a thin convex lens of focal length 30 cm. A convex spherical mirror of radius of curvature 100 cm is placed to the right of the lens at a distance of 50 cm. The mirror is tilted such that the axis of the mirror is at an angle …

Consider a concave mirror and a convex lens (refractive index = 1.5) of focal length 10 cm each, separated by a distance of 50 cm in air (refractive index = 1) as shown in the figure. An object is placed at a distance of 15 cm from the mirror. Its erect image formed by this combi …

Two idenctical glass rods ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ (refractive index = 1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance $d$ as shown in the figure, with their axes (shown by the dashed line) aligned. When a …

A monochromatic beam of light is incident at 60° on one face of an equilateral prism of refractive index $n$ and emerges from the opposite face making an angle $\theta (n)$ with the normal (see the figure). For $n=\sqrt{3}$ the value of $\theta$ is $60^{\circ }$ and …

PARAGRAPH 2

Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index $n_1$ surrounded by a medium of lower refractive index $n_2$. The light guidance in the structure takes place due to su …

PARAGRAPH 2

Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index $n_1$ surrounded by a medium of lower refractive index $n_2$. The light guidance in the structure takes place due to su …

A point source $S$ is placed at the bottom of a transparent block of height $10mm$ and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright sp …

Four combinations of two thin lenses are given in List I. The radius of curvature of all curved surfaces is $r$ and the refractive index of all the lenses is 1.5. Match lens combinations in List I with their focal length in List II and select the correct answer using the code g …

A transparent thin film of uniform thickness and refractive index $n_1=1.4$ is coated on the convex spherical surface of radius Rat one end of a long solid glass cylinder of refractive index $n_2=1.5$, as shown in the figure. Rays of light parallel to the axis of the cyli …

A ray of light travelling in the direction $\frac{1}{2}(\hat{i}+\sqrt{3}\hat{j})$ is incident on a plane mirror. After reflection, it travels along the direction $\frac{1}{2}(\hat{i}-\sqrt{3}\hat{j})$. The angle of incidence is

The image of an object, formed by a plano-convex lens at a distance of $8m$ behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is $\frac{2}{3}$ times the wavelength in free space. The radius of the curved surface of the …

A right angled prism of refractive index ${\mu }_1$ is placed in a rectangular block of refractive index ${\mu }_2$, which is surrounded by a medium of refractive index ${\mu }_3$, as shown in the figure. A ray of light 'e' enters the rectangular block at normal incidence. Dep …

A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index $n$ of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surfaces are of the same radius of curvature $R=14\mathrm{cm}$. For this bi-convex lens, fo …

Most materials have the refractive index, $n>1$. So, when a light ray from air enters a naturally occurring material, then by Snell's law, $\frac{\sin {\theta }_1}{\sin {\theta }_2}=\frac{n_2}{n_1}$, it is understood that the refracted ray bends towards the normal. But it n …

Most materials have the refractive index, $n>1$. So, when a light ray from air enters a naturally occurring material, then by Snell's law, $\frac{\sin {\theta }_1}{\sin {\theta }_2}=\frac{n_2}{n_1}$, it is understood that the refracted ray bends towards the normal. But it n …

A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence $\theta$. The reflected ( R ) and transmitted ( T ) intensities, both as function of $\theta$, are plotted. The correct sketch is

Water (with refractive index $=\frac{4}{3}$ ) in a tank is 18 cm deep. Oil of refractive index $\frac{7}{4}$ lies on water making a convex surface of radius of curvature ' $\mathrm{R}=6\mathrm{cm}$ ' as shown. Consider oil to act as a thin lens. An object ' S ' is placed …

A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of $60^{\circ }$ (see figure). If the refractive index of the material of the prism is $\sqrt{3}$, which of the following is (are) correct ?

The focal length of a thin biconvex lens is 20cm. When an object is moved from a distance of 25cm in front of it to 50cm, the magnification of its image changes from $m_{25}$ to $m_{50}$. The ratio $\frac{m_{25}}{m_{50}}$ is