Two identical thin plano-convex glass lenses (refractive index $1.5)$ each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index $1.7.$ The focal length of the combination is

An 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

The angle of incidence for a ray of light at a refracting surface of a prism is 45°. The angle of prism is 60°. 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

Match the corresponding entries of Column I with Column II (where m is the magnification produced by the mirror)

The ratio of resolving powers of an optical microscope for two wavelengths $\lambda_1 = 4000$ Å and $\lambda_2 = 6000$ Å is

A thin prism having refracting angle 10° 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 the second prism should be

Young’s double-slit experiment is first performed in air and then in a medium other than air. It is found that 8th bright fringe in the medium lies where 5th dark fringe lies in air. The refractive index of the medium is nearly

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

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 $30^{\circ}.$ 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

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

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?

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 $(\mu = 1.5)$, the equivalent focal length is $F_2.$ The ratio $F_1 : F_2$ will be:

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 the angle of refraction?

Which colour of the light has the longest wavelength?

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:

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:

The Brewster’s angle $i_b$ for an interface should be:

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 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:

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

Find the value of the angle of emergence from the prism. Refractive index of the glass is $\sqrt{3}.$

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 $\sqrt{3},$ at an angle $60^\circ.$ 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:

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?

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 the 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 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:

A small telescope has an objective of focal length 120 cm and an eye piece of focal length 5.0 cm. The magnifying power of telescope for viewing a distant object is: