Ray Optics and Optical Instruments PYQs

A ray of monochromatic light is passing through an equilateral prism (ABC) as shown in the figure. The refracted ray (QR) is parallel to its base (BC) and the angle of incidence (i) is 50°. Then the angle of deviation (δ) is:

In a concave lens, a ray of light emanating from the object parallel to the principal axis of the lens after refraction:

A microscope has an objective of focal length 2 cm, eyepiece of focal length 4 cm and the tube length of 40 cm. If the distance of distinct vision of eye is 25 cm, the magnification in the microscope is

In a certain camera, a combination of four similar thin convex lenses are arranged axially in contact. Then the power of the combination and the total magnification in comparison to the power (p) and magnification (m) for each lens will be, respectively –

A light ray enters through a right angled prism at point P with the angle of incidence 30° as shown in figure. It travels through the prism parallel to its base BC and emerges along the face AC. The refractive index of the prism is:

A small telescope has an objective of focal length 140 cm and an eye piece of focal length 5.0 cm. The magnifying power of telescope for viewing a distant object is:

Light travels a distance x in time $t_1$ in air and 10x in time $t_2$ in another denser medium. What is the critical angle for this medium?

Two thin lenses are of same focal lengths (f), but one is convex and the other is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be :

In the figure shown here, what is the equivalent focal length of the combination of lenses (Assume that all layers are thin)?

A biconvex lens has radii of curvature, 20 cm each. If the refractive index of the material of the lens is 1.5, the power of the lens is

A light ray falls on a glass surface of refractive index √3, at an angle 60°. The angle between the refracted and reflected rays would be:

Two transparent media A and B are separated by a plane boundary. The speed of light in those media are 1.5 × 10⁸ m/s and 2.0 × 10⁸ m/s, respectively. The critical angle for a ray of light for these two media is:

A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since

A convex lens 'A' of focal length 20 cm and a concave lens 'B' of focal length 5 cm are kept along the same axis with a distance d between them. If a parallel beam of light falling on 'A' leaves 'B' as a parallel beam, then 'd' is:

Find the value of the angle of emergence from the prism. Refractive index of the glass is √3.

A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror is kept perpendicular to the principal axis and at a distance of 40 cm from the lens, the final image would be formed at a distance of:

A ray is incident at an angle of incidence i on one surface of a small angle prism (with angle prism A) and emerges normally from the opposite surface. If the refractive index of the material of the prism is μ, then the angle of incidence is nearly equal to :

Assume that light of wavelength 600 nm is coming from a star. The limit of resolution of a telescope whose objective has a diameter of 2 m is :

An equiconvex lens has power $P$. It is cut into two symmetrical halves by a plane containing the principal axis. The power of one part will be:

A double convex lens has focal length $25\ \text{cm}$. The radius of curvature of one of the surfaces is double of the other. Find the radii if the refractive index of the material of the lens is $1.5$.

An astronomical refracting telescope will have large angular magnification and high angular resolution, when it has an objective lens of:

The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is 30°. One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is:

An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be:

The ratio of resolving powers of an optical microscope for two wavelengths $\lambda_1 = 4000\,\text{\AA}$ and $\lambda_2 = 6000\,\text{\AA}$ is:

A thin prism having refracting angle $10^\circ$ is made of glass of refractive index $1.42$. This prism is combined with another thin prism of glass of refractive index $1.7$. The combination produces dispersion without deviation. The refracting angle of the second prism should be:

A beam of light from a source $L$ is incident normally on a plane mirror fixed at a distance $x$ from the source. The beam is reflected back as a spot on a scale placed just above the source $L$. When the mirror is rotated through a small angle $\theta$, the spot of light is found to move through a distance $y$ on the scale. The angle $\theta$ is given by:

Two identical glass $(\mu_g = 3/2)$ equiconvex lenses of focal length $f$ are kept in contact. The space between the two lenses is filled with water $(\mu_w = 4/3)$. The focal length of the combination is:

An air bubble in a glass slab with refractive index $1.5$ (near normal incidence) is $5\ \text{cm}$ deep when viewed from one surface and $3\ \text{cm}$ deep when viewed from the opposite face. The thickness of the slab is:

A person can see clearly objects only when they lie between $50\ \text{cm}$ and $400\ \text{cm}$ from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be:

In an astronomical telescope in normal adjustment, a straight black line of length $L$ is drawn on the inside part of the objective lens. The eyepiece forms a real image of this line. The length of this image is $l$. The magnification of the telescope is:

A beam of light consisting of red, green and blue colours is incident on a right-angled prism. The refractive indices of the material of the prism for the red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. The prism will:

If the focal length of objective lens is increased, then magnifying power of:

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 return back through the same path after suffering reflection at the silvered surface. The refractive index μ of the prism is:

A plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices $\mu_1$ and $\mu_2$, and $R$ is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is

For a normal eye, the cornea of eye provides a converging power of $40\,D$ and the eye lens behind the cornea is $20\,D$. Using this information, the distance between retina and the cornea-eye lens system can be estimated to be

For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index:

A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its end closer to the pole is 20 cm away from the mirror. The length of the image is:

A thin prism of angle 15° made of glass of refractive index μ₁ = 1.5 is combined with another prism of glass of refractive index μ₂ = 1.75. The combination of the prism produces dispersion without deviation. The angle of the second prism should be:

A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side. If the lens is removed the point where the rays would meet moves 5 cm closer to the lens. The focal length of the lens is:

The speed of light in media $M_1$ and $M_2$ are $1.5 \times 10^8\ \text{m/s}$ and $2.0 \times 10^8\ \text{m/s}$ respectively. A ray of light enters from medium $M_1$ to $M_2$ at an incidence angle i. If the ray suffers total internal reflection, the value of i is

A ray of light is incident on a 60° prism at the minimum deviation position. The angle of refraction at the first face (or the angle of incidence at the second face) of the prism is

Two thin lenses of focal lengths f₁ and f₂ are in contact and coaxial. The power of the combination is

A boy is trying to start a fire by focusing Sunlight on a piece of paper using an equiconvex lens of focal length 10 cm. The diameter of the Sun is 1.39 × 10⁹ m and its mean distance from the earth is 1.5 × 10¹¹ m. What is the diameter of the Sun's image on the paper?

A microscope is focussed on a mark on a piece of paper and then a slab of glass of thickness 3 cm and refractive index 1.5 is placed over the mark. How should the microscope be moved to get the mark in focus again?

A convex lens and a concave lens, each having same focal length of 25 cm, are put in contact to form a combination of lenses. The power in diopters of the combination is:

The angular resolution of a 10 cm diameter telescope at wavelength 5000 Å is of the order of: