Optics PYQ — Page 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

An equi-convex 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

Angular width of the central maxima in the Fraunhoffer diffraction for $\lambda=6000 Å$ is $\theta_0$. When the same slit is illuminated by another monochromatic light, the angular width decreases by $30 \%$. The wavelength of this light is

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.

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?

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 ${0.21}^{o}$ (with same $\lambda \text{and} D$) 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

The refractive index of the materiel of a prism is $\sqrt{2}$ and the angle of the prism is ${30}^{o}.$ One of the two refracting surface 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 plane surface of a material of refractive index $\mu$. At a particular angle of incident $i$ it is found that the reflected and refracted rays are perpendicular to each other. Which of the following options is correct for this situation?

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

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

The ratio of resolving powers of an optical microscope for two wavelengths ${\lambda }_{1}=4000 Å$ and ${\lambda }_{2}=6000 Å$ is

Two Polaroids ${P}_{1}$ and ${P}_{2}$ are placed with their axis perpendicular to each other. Unpolarised light with intensity ${I}_{0}$ 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 ${45}^{\text{o}}$ with that of ${P}_{1}$. The intensity of transmitted light through ${P}_{2}$ 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

Match the corresponding entries of column 1 with column 2. [Where m is the magnification produced by the mirror]<table class="pyq-table"><tbody><tr><td></td><td>Column 1</td><td></td><td>Column 2</td></tr><tr><td>(A)</td><td>$m=-2$</td><td>(a)</td><td>Convex mirror</td></tr><tr><td>(B)</td><td>$m=-\frac{1}{2}$</td><td>(b)</td><td>Concave mirror</td></tr><tr><td>(C)</td><td>$m=+2$</td><td>(c)</td><td>Real image</td></tr><tr><td>(D)</td><td>$m=+\frac{1}{2}$</td><td>(d)</td><td>Virtual image</td></tr></tbody></table>

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

A person can see clearly object only when they lie between $50\mathrm{cm}$ to $400\mathrm{cm}$ 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 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:

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 $5\times {10}^{-5} cm$. The distance of the first dark band of the diffraction pattern from the centre of the screen is

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 $D=10d$?

In a diffraction pattern due to a single slit of width $a$ the first minimum is observed at an angle ${30}^{o}$ when light of wavelength $5000 Å$ is incident on the slit. The first secondary maximum is observed at an angle of:

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

The angle of incidence for a ray of light at a refracting surface of a prism is ${45}^{o}$. The angle of prism is ${60}^{o}$. 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: