Ray Optics

Water (with refractive index $=\frac43$) in a tank is 18 cm deep. Oil of refractive index $\frac74$ lies on water making a convex surface of radius of curvature '$R=6$ cm' as shown. Consider oil to act as a thin lens. An object 'S' is placed 24 cm above water surface. The location of its image is at '$x$' cm above the bottom of the tank. Then '$x$' is

A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60° (see figure). If the refractive index of the material of the prism is $\sqrt3$, 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 $\dfrac{m_{25}}{m_{50}}$ is

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

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

A large glass slab ($\mu=5/3$) of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius $R$ cm. What is the value of $R$?

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 diagrams shown in Column II.

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 $g=10\ \mathrm{m/s^2}$.]

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 meter. 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)

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

A light beam is traveling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are $n_0$, $\frac{n_0}2$, $\frac{n_0}6$ and $\frac{n_0}8$, 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 × 4 matrix given in the ORS.

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 $x$ from the pole P. The student looks at the pin and its inverted image from 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 of the object pin. Then,

A ray of light traveling in water is 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.

because

STATEMENT-2: Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

Speed of light is