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A rod of length $10\text{ cm}$ lies along the principal axis of a concave mirror of focal length $10\text{ cm}$ in such a way that its end closer to the pole is $20\text{ cm}$ away from the mirror. The length of the image is:
A small coin is resting on the bottom of a beaker filled with a liquid. A ray of light from the coin travels up, to the surface of the liquid and moves along its surface (see figure). How fast is the light traveling in the liquid?
If the critical angle for total internal reflection from a medium to vacuum is $45^{\circ}$, the velocity of light in the medium is:
A microscope is focused on a mark on a piece of paper and then a slab of glass of thickness $3 \text{ cm}$ and a refractive index $1.5$ is placed over the mark. How should the microscope be moved to get the mark in focus again?
A ray of light is incident at an angle of incidence, $i$, on one face of a prism of angle $A$ (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is $\mu$, the angle of incidence $i$, is nearly equal to:
The refracting angle of a prism is $A$, and the refractive index of the material of the prism is $\cot(A/2)$. The angle of minimum deviation is:
For a normal eye, the cornea of eye provides a converging power of $40\text{ D}$ and the least converging power of the eye lens behind the cornea is $20\text{ D}$. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be:
Three blocks with masses $m$, $2m$, and $3m$ are connected by strings as shown in the figure. After an upward force $F$ is applied on block $m$, the masses move upward at constant speed $v$. What is the net force on the block of mass $2m$? ($g$ is the acceleration due to gravity)
The displacement-time ($x-t$) graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $t = 2$ s is:
The angle of a prism is $A$. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence $2A$ on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index $\mu$ of the prism is:
Match the corresponding entries of Column 1 (Magnification, m) with Column 2 (Nature of Mirror/Image): **Column 1** (A) m = –2 (B) m = –1/2 (C) m = +2 (D) m = +1/2 **Column 2** (a) Convex mirror (b) Concave mirror (c) Real image (d) Virtual image
Which of the following is not due to total internal reflection?
A car is negotiating a curved road of radius $R$. The road is banked at an angle $\theta$. The coefficient of friction between the tyre of the car and the road is $\mu_s$. The maximum safe velocity on this road is:
The given electrical network is equivalent to:
An astronomical refracting telescope will have large angular magnification and high angular resolution when it has an objective lens of:
A concave lens with a focal length of $-25 \text{ cm}$ is sandwiched between two convex lenses, each with a focal length of $40 \text{ cm}$. The power (in diopters) of the combined lens system would be:
For the given circuit, the input digital signals are applied at the terminals A, B and C. What would be the output at terminal Y?
A light ray falls on a glass surface of refractive index $\sqrt{3}$, at an angle of $60^{\circ}$. The angle between the refracted and reflected rays would be:
A convex lens A of focal length $20\text{ cm}$ and a concave lens B of focal length $5\text{ cm}$ are kept along the same axis with the distance $d$ between them. If a parallel beam of light falling on A leaves B as a parallel beam, then distance $d$ in cm will be:
A ray of light is incident on a $60^{\circ}$ prism at the minimum deviation position. The angle of refraction at the first face (i.e., incident face) of the prism is: