Optics 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 interference and diffraction, the light energy is redistributed. If it reduces in one region, producing a dark fringe, it increases in another region, producing a bright fringe. A. As there is no gain or loss of energy, these phenomena are consistent with the principle of conservation of energy. B. Diffraction and interference are characteristics exhibited only by light waves. Choose the correct answer from the options given below:

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 –

An unpolarized light beam travelling in air is incident on a medium of refractive index 1.73 at Brewster’s angle. Then-

The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at 22.5° from the polarization axis of one of the polaroid, is ($I_0$ is the intensity of polarized light after passing through the first polaroid):

If the monochromatic source in Young’s double slit experiment is replaced by white light, then

An unpolarised light beam strikes a glass surface at Brewster’s angle. Then:

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?

For Young’s double slit experiment, two statements are given below: Statement I : If screen is moved away from the plane of slits, angular separation of the fringes remains constant. Statement II : If the monochromatic source is replaced by another monochromatic source of larger wavelength, the angular separation of fringes decreases. In the light of the above statements, choose the correct answer from the options given below:

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

In a Young's double slit experiment, a student observes 8 fringes in a certain segment of screen when a monochromatic light of 600 nm wavelength is used. If the wavelength of light is changed to 400 nm, then the number of fringes he would observe in the same region of the screen 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:

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

The Brewster angle i$_b$ for an interface should be

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 :

In Young’s double slit experiment, if the separation between coherent sources is halved and the distance of the screen from the coherent sources is doubled, then the fringe width becomes :

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 :

Angular width of the central maxima in the Fraunhofer diffraction for λ = 6000 Å is θ₀. When the same slit is illuminated by another monochromatic light, the angular width decreases by 30%. The wavelength of this light 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:

In a Young’s double slit experiment, if there is no initial phase difference between the light from the two slits, a point on the screen corresponding to the fifth minimum has path difference:

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 $1.5$.

In Young's double slit experiment the separation between the slits is 2 mm, the wavelength λ of the light used is 5896 Å and distance D between the screen and slits is 100 cm. It is found that the angular width of fringes is 0.20°. To increase the fringe angular width to 0.21° (with same λ and D) the separation between the slits needs to be changed to:

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

Unpolarised light is incident from air on a plane surface of a material of refractive index 'μ'. At a particular angle of incidence 'i', it is found that the reflected and refracted rays are perpendicular to each other. Which of the following options is correct for this situation?

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:

Two Polaroids $P_1$ and $P_2$ are placed with their transmission axes perpendicular to each other. Unpolarised light of intensity $I_0$ is incident on $P_1$. A third Polaroid $P_3$ is placed between $P_1$ and $P_2$ such that its axis makes an angle $45^\circ$ with that of $P_1$. The intensity of transmitted light through $P_2$ is:

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:

Young's double slit experiment is first performed in air and then repeated in a medium other than air. It is found that the eighth bright fringe in the medium lies where the fifth dark fringe lies in air. The refractive index of the medium is nearly:

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:

The interference pattern is obtained with two coherent light sources of intensity ratio $n$. In the interference pattern, the ratio $$\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$$ will be:

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:

A linear aperture whose width is $0.02\ \text{cm}$ is placed immediately in front of a lens of focal length $60\ \text{cm}$. The aperture is illuminated normally by a parallel beam of wavelength $5 \times 10^{-5}\ \text{cm}$. The distance of the first dark band from the centre of the screen is:

At the first minimum adjacent to the central maximum of a single-slit diffraction pattern, the phase difference between the Huygens wavelet from the edge of the slit and the wavelet from the mid-point of the slit is:

A beam of light of λ = 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between first dark fringes on either side of the central bright fringe is:

In the Young's double-slit experiment, the intensity of light at a point on the screen where the path difference is λ is K, λ being the wavelength of light used. The intensity at a point where the path difference is λ/4 will be:

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 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: