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_L. The correct plot showing the variation of the power, in the units of diopter (D), as a function of n_L is :

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 mirrors and perpendicular to their common principal axis. A monochromatic point light source S is embedded at the center of the slab on the principal axis, as shown in the schematic diagram. For the image to be formed on S itself, which of the following distances between the two mirrors is/are correct:

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 with a liquid of refractive index $n$ up to the level QPR. If the image of a point object $\mathrm{O}$ at a height of $h$ (OT in the figure) is formed onto itself, then, which of the following option(s) is(are) correct?

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 reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is $\alpha$. Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

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 hole. The cross section of the mirror configuration and the ray of light lie on the same plane.

Which of the following statement(s) is(are) correct?

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 the two lenses is $5 \mathrm{~cm}$. List II contains the positions of the final images.

List-I	List-II
(I)	(P) Final image is formed at $7.5 \mathrm{~cm}$ on the right side of lens 2 .
(II)	(Q) Final image is formed at $60.0 \mathrm{~cm}$ on the right side of lens 2 .
(III)	(R) Final image is formed at $30.0 \mathrm{~cm}$ on the left side of lens $2 .$
(IV)	(S) Final image is formed at $6.0 \mathrm{~cm}$ on the right side of lens 2 .
	(T) Final image is formed at $30.0 \mathrm{~cm}$ on the right side of lens 2 .

Which one of the following options is correct?

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 the liquid forms a circular bright spot of diameter 11.54 mm on the top of the block. The refractive index of the liquid is

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 given below the lists.

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. Depending upon the relationships between $\mu$₁, $\mu$₂ and $\mu$₃, it takes one of the four possible paths 'ef', 'eg', 'eh' or 'ei'.

Match the paths in List I with conditions of refractive indices in List II and select the correct answer using the codes given below the lists:

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 ${1 \over 2}\left( {\widehat i - \sqrt 3 \widehat j} \right)$. The angle of incidence is

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

Choose the correct statement.

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 biconvex lens, for an object distance of 40 cm, the image distance will be

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 $\sqrt3$, which of the following is(are) correct?

A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is

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 figures. In Column I different relationships between $\mu_1, \mu_2$ and $\mu_3$ are given. Match them to the ray diagram shown in Column II :

A student performed the experiment of determination of focal length of a concave mirror by $u$-$v$ method using an optical bench of length 1.5 m. The focal length of the mirror used is 24 cm. The maximum error in the location of the image can be 0.2 cm. The 5 sets of ($u,v$) values recorded by the student (in cm) are : (42, 56), (48, 48), (60, 40), (66, 33), (78, 39). The data set(s) that cannot come from experiment and is (are) incorrectly recorded, is (are)

A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as (Take g = 10 m/s$^2$)

A light beam is travelling from Region I to Region IV (Refer figure). The refractive index in Regions I, II, III and IV are ${n_0},{{{n_0}} \over 2},{{{n_0}} \over 6}$ and ${{{n_0}} \over 8}$, respectively. The angle of incidence $\theta$ for which the beam just misses entering Region IV is

An optical component and an object S placed along its optic axis are given in Column I. The distance between the object and the component can be varied. The properties of images are given in Column II. Match all the properties of images from Column II with the appropriate components given in Column I. Indicate your answer by darkening the appropriate bubbles of the 4 $\times$ 4 matrix given in the ORS.

	Column I		Column II
(A)		(P)	Real Image
(B)		(Q)	Virtual Image
(C)		(R)	Magnified Image
(D)		(S)	Image at infinity

Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is 60$^\circ$). In the position of minimum deviation, the angle of refraction will be :

Light travels as a

The phases of the light wave at $c, d, e$ and $f$ are $\phi_c, \phi_d, \phi_{e}$ and $\phi_{f}$ respectively.

It is given that $\phi_{c} \neq \phi_{f}$.

In an experiment to determine the focal length (f) of a concave mirror by the u-v method, a student places the object pin A on the principal axis at a distance x form the pole P. The student looks at the pin and its inverted image form a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right, oh the object pin. Then,

A ray of light travelling in water in incident on its surface open to air. The angle of incidence is $\theta$, which is less than the critical angle. Then there will be

Statement 1 :

The formula connecting u, v and f for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.

Statement 2 :

Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm , if the plane surface is silvered. The image will form at

A biconvex lens of focal length $f$ forms a circular image of sun of radius $r$ in focal plane. Then

Graph of position of image versus position of point object from a convex lens is shown. Then, the focal length of the lens is

A simple telescope used to view distant objects has eyepiece and objective lens of focal lengths $f_e$ and $f_0$, respectively. Match Column I with Column II:

What will be the minimum angle of incidence such that the total internal reflection occurs on both the surfaces?

Two identical prisms of refractive index $\sqrt{3}$ are kept as shown in the figure. A light ray strikes the first prism at face AB. Find

(A) the angle of incidence so that the emergent ray from the first prism has minimum deviation;

(B) through what angle, the prism DCE should be rotated about C so that the final emergent ray also has minimum deviation?