Optics

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 \(22.5^\circ\) from the polarization axis of one of the polaroid, is (\(I_0\) is the intensity of polarised light after passing through the first polaroid):

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 \(30^\circ\) 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:

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

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:

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

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

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 \(\sqrt{3}\), 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 \(1.5 \times 10^{8}\) m/s and \(2.0 \times 10^{8}\) 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 \(\sqrt{3}\).

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 the distance 'd' in cm will be :

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

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

The Brewsters 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 of prism A) and emerges normally from the opposite surface. If the refractive index of the material of the prism is \(\mu\), 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 telescope whose objective has a diameter of 2 m is :

In a double slit experiment, when light of wavelength 400 nm was used, the angular width of the first minima formed on a screen placed 1 m away, was found to be \(0.2^\circ\). What will be the angular width of the first minima, if the entire experimental apparatus is immersed in water ? (\(\mu_{water} = 4/3\))

Two similar thin equi-convex lenses, of focal length \(f\) each, are kept coaxially in contact with each other such that the focal length of the combination is \(F_1\). When the space between the two lenses is filled with glycerin (which has the same refractive index (\(\mu = 1.5\)) as that of glass) then the equivalent focal length is \(F_2\). The ratio \(F_1 : F_2\) will be :

Pick the wrong answer in the context with rainbow.

In total internal reflection when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be angle of refraction ?

Unpolarised light is incident from air on a plane surface of a material of refractive index '\(\mu\)'. 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 ?

In Young's double slit experiment the separation d between the slits is 2 mm, the wavelength \(\lambda\) 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 the fringes is \(0.20^\circ\). To increase the fringe angular width to \(0.21^\circ\) (with same \(\lambda\) 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

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 refractive index of the material of a prism is \(\sqrt2\) and the angle of the prism is \(30^\circ\). 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

Young's double slit experiment is first performed in air and then in a medium other than air. It is found that \(8^{th}\) bright fringe in the medium lies where \(5^{th}\) dark fringe lies in air. The refractive index of the medium is nearly :

The ratio of resolving powers of an optical microscope for two wavelengths \(\lambda_1\) = 4000 \(\mathrm{\AA}\) and \(\lambda_2\) = 6000 \(\mathrm{\AA}\) 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. This combination produces dispersion without deviation. The refracting angle of second prism should be :

A beam of light from a source L is incident normally on a plane mirror fixed at a certain 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 the light is found to move through a distance \(y\) on the scale. The angle \(\theta\) is given by :

Two Polaroids \(P_1\) and \(P_2\) are placed with their axis perpendicular to each other. Unpolarised light \(I_0\) is incident on \(P_1\). A third polaroid \(P_3\) is kept in 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 :

In a diffraction pattern due to a single slit of width 'a', the first minimum is observed at an angle \(30^\circ\) when light of wavelength 5000 Å is incident on the slit. The first secondary maximum is observed at an angle of :

The intensity at the maximum in a Young's double slit experiment is \(I_0\). Distance between two slits is \(d = 5\lambda\), where \(\lambda\) is the wavelength of light used in the experiment. What will be the intensity in front of one of the slits on the screen placed at a distance \(D = 10\,d\) ?

The angle of incidence for a ray of light at a refracting surface of a prism is \(45^\circ\). The angle of prism is \(60^\circ\). If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are :

A astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance :

Match the corresponding entries of column 1 with column 2. [Where m is the magnification produced by the mirror]

Column 1: (A) \(m = -2\); (B) \(m = -\frac{1}{2}\); (C) \(m = +2\); (D) \(m = +\frac{1}{2}\)

Column 2: (a) Convex mirror; (b) Concave mirror; (c) Real image; (d) Virtual image

Two identical glass (\(\mu_g=3/2\)) equiconvex lenses of focal length \(f\) each 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 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness (in cm) 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 cm and 400 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 cm is placed immediately in front of a lens of focal length 60 cm. The aperture is illuminated normally by a parallel beam of wavelength \(5\times10^{-5}\) cm. The distance of the first dark band of the diffraction pattern from the centre of the screen is