Geometrical Optics

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 mirr...

A beam of polychromatic light passes through a thin prism of prism angle $6^{\circ}$. The refractive index of the material of the prism varies with wavelength $(\lambda)$ as $n(\lambda) = \alpha \lambda + \frac{\beta}{\lambda^2}$, where $\a...

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 nL. The correct plot showing the variation of the power, in the units of diopter...

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 equid...

A solid glass sphere of refractive index $n=\sqrt{3}$ and radius $R$ contains a spherical air cavity of radius $\frac{R}{2}$, as shown in the figure. A very thin glass layer is present at the point 0 so that the air cavity (refractive index...

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...

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 $\phi_0$ and then partly reflects from the back surface. The...

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 $9 \mathrm{~cm}$, while the planar surface (STU) acts as a mirror. This beaker is filled ...

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 $n_1$ to $n_2$ over the height $h$. Which of the following statement(s) is(ar...

An optical arrangement consists of two concave mirrors $M_1$ and $M_2$, and a convex lens $L$ with a common principal axis, as shown in the figure. The focal length of $\mathrm{L}$ is $10 \mathrm{~cm}$. The radii of curvature of $M_1$ and $...

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...

An object and a concave mirror of focal length $f=10 \mathrm{~cm}$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_{0}=15 \mathrm{~cm} \mathrm{~s}^{-1}$ towards the mirror with respect t...

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

List I contains four combinations of two lenses (1 and 2) whose focal lengths (in $\mathrm{cm}$ ) are indicated in the figures. In all cases, the object is placed $20 \mathrm{~cm}$ from the first lens on the left, and the distance between t...

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 ...

A rod of length $2 \mathrm{~cm}$ makes an angle $\frac{2 \pi}{3} \mathrm{rad}$ with the principal axis of a thin convex lens. The lens has a focal length of $10 \mathrm{~cm}$ and is placed at a distance of $\frac{40}{3} \mathrm{~cm}$ from t...

For a prism of prism angle \(\theta\) = 60\(^\circ\), the refractive indices of the left half and the right half are, respectively, n1 and n2 (n2 \(\ge\) n1) as shown in the figure. The angle of incidence i is chosen such that the incident ...

A wide slab consisting of two media of refractive indices n1 and n2 is placed in air as shown in the figure. A ray of light is incident from medium n1 to n2 at an angle \(\theta\), where sin\(\theta\) is slightly larger than 1/n1. Take refr...

An extended object is placed at point O, 10 cm in front of a convex lens L1 and a concave lens L2 is placed 10 cm behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses ae 20 cm. The refracti...

A beaker of radius r is filled with water (refractive index \({4 \over 3}\)) 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 ...

A large square container with thin transparent vertical walls and filled with water
(refractive index \({4 \over 3}\)) is kept on a horizontal table. A student holds a thin straight wire vertically
inside the water 12 cm from one of its cor...

A monochromatic light is incident from air on a refracting surface of a prism of angle 75\(^\circ\) and refractive index \({n_0} = \sqrt 3\). The other refracting surface of the prism is coated by a thin film of material of refractive ind...

Three glass cylinders of equal height H = 30 cm and same refractive index n = 1.5 are placed on a horizontal surface as shown in figure. Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii ...

A thin convex lens is made of two materials with refractive indices n1 and n2, as shown in the figure. The radius of curvature of the left and right spherical surfaces are equal. f is the focal length of the lens when n1 = n2 = n. The focal...

A planar structure of length L and width W is made of two different optical media of refractive indices n1 = 1.5 and n2 = 1.44 as shown in figure. If L >> W, a ray entering from end AB will emerge from end CD. CD only if the total internal ...

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 ima...

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

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...

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 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 ax...

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 n1 and n2 (>...

A parallel beam of light is incident from air at an anglea 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 a has a mi...

A plano-convex lens is made of 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 sur...

A monochromatic beam of light is incident at 60\(^\circ\) 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 figure). For n = \(\sqrt 3\) the valu...

If two structures of same cross-sectional area, but different numeral apertures NA1 and NA2 (NA2 < NA1) are joined longitudinally, the numerical aperture of the combined structure is

For two structures namely S1 with n1 = \({{\sqrt {45} } \over 4}\) and n2 = \({3 \over 2}\), and S2 with n1 = \({8 \over 5}\) and n2 = \({7 \over 5}\) and taking the refractive index of water to be \({4 \over 3}\) and that to air to be 1, t...

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 mirr...

Two identical glass rods S1 and S2 (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) aligne...

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...

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

A transparent thin film of uniform thickness and refractive index n1 = 1.4 is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index n2 = 1.5, as shown in the figure. Rays of light ...

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 b...

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

A ray of light travelling in the direction \({1 \over 2}\left( {\widehat i + \sqrt 3 \widehat j} \right)\) is incident on a plane mirror. After reflection, it travels along the direction $${1 \over 2}\left( {\widehat i - \sqrt 3 \widehat j}...

Choose the correct statement.

For light incident from air on a meta-material, the appropriate ray diagram is

A biconvex lens is formed with two planoconvex 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 curved surface are of the same radius of curvature R = 14 cm. For this biconv...

Water (with refractive index = 4/3) in a tank is 18 cm deep. Oil of refractive index 7/4 lies on water making a convex surface of radius of curvature R = 6 cm as shown. Consider oil to act a thin lens. An object S is placed 24 cm above wate...

Two transparent media of refractive indices $\mu_1$ and $\mu_3$ have a solid lens shaped transparent material of refractive index $\mu_2$ between them as shown in figures in Column II. A ray traversing these media is also shown in the figur...

Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from \({{25} \over 3}\) m to \({{50} \over 7}\) m in 30 s. What is the speed of the object in km per hour?