Optics PYQ — Page 15

A polarizer - analyser set is adjusted such that the intensity of light coming out of the analyser is just $36%$ of the original intensity. Assuming that the polarizer - analyser set does not absorb any light, the angle by which the analyser needs to be rotated further, to reduce the output intensity to zero, is $({\mathrm{sin}}^{-1}(\frac{3}{5})=37^{\circ})$

In a double – slit experiment, at a certain point on the screen the path difference between the two interfering waves is $\frac{1}{8}th$ of a wavelength. The ratio of the intensity of light at that point to that at the center of a bright fringe is:

A point like object is placed at distance of $1m$ in front of a convex lens of focal length $0.5m$. A plane mirror is placed at a distance of $2m$ behind the lens. The position and nature of the image formed by the system is

When an object is kept at a distance of $30\mathrm{cm}$ from a concave mirror, the image is formed at a distance of $10\mathrm{cm}$from the mirror. If the object is moved with a speed of $9\mathrm{cm}{s}^{-1}$ , the speed (in $\mathrm{cm}{s}^{-1}$) with which image moves at that instant is

In the figure below, $P$ and $Q$ are two equally intense coherent sources emitting radiation of wavelength $20m.$ The separation between $P$ and $Q$ is $5m$ and the phase of $P$ is ahead of that of $Q$ by $90^{\circ}.A,B$ and C are three distinct point of observation, each equidistant from the midpoint of PQ. The intensities of radiation at $A,B,C$ will be in the ratio : 

The magnifying power of a telescope with tube length $60cm$ is $5.$ What is the focal length of its eye piece?

The distance between an object and a screen is $100\mathrm{cm}$. A lens can produce real image of the object on the screen for two different positions between the screen and the object. The distance between these two positions is $40\mathrm{cm}$. If the power of the lens is close to $(\frac{N}{100})D$ where $N$ is an integer, the value of $N$ is _________

A beam of plane polarized light of large cross-sectional area and uniform intensity of $3.3W{m}^{–2}$ falls normally on a polarizer (cross-sectional area $3\times {10}^{–4}{m}^{2}$), which rotates about its axis with an angular speed of $31.4\mathrm{rad}{s}^{-1}$. The energy of light passing through the polarizer per revolution, is close to:

An upright object is placed at a distance of $40 cm$ in front of a convergent lens of focal length $20 cm.$ A convergent mirror of focal length $10 cm$ is placed at a distance of $60 cm$ on the other side of the lens. The position and size of the final image will be:

A system of three polarizers ${P}_{1},{P}_{2},{P}_{3}$ is set up such that the pass axis of ${P}_{3}$ is crossed with respect to that of ${P}_{1}$ . The pass axis of ${P}_{2}$ is inclined at ${60}^{o}$ to the pass axis of ${P}_{3}.$ When a beam of unpolarized light of intensity ${I}_{o}$ is incident on ${P}_{1},$ the intensity of light transmitted by the three polarizers is $I$ . The ratio $({I}_{o}/I)$ equals (nearly):

The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of the cornea $(7.8 \mathrm{mm})$. This surface separates two media of refractive indices $1$ and $1.34$. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.

A thin convex lens $L$ (refractive index $=1.5$ ) is placed on a plane mirror $M$. When a pin is placed at $A$, such that $OA=18 cm,$ its real inverted image is formed at $A$ itself, as shown in figure. When liquid of refractive index ${\mu }_{l}$ is put between the lens and the mirror, the pin has to be moved to ${A}^{'},$ such that $O{A}^{'}=27 cm,$ to get its inverted real image at $A'$ itself. The value of ${\mu }_{l}$ will be 

In a double-slit experiment, green light $(5303 \mathrm{~A})$ falls on a double slit having a separation of $19.44 \mu \mathrm{m}$ and a width of $4.05 \mu \mathrm{m}$. The number of bright fringes between the first and the second diffraction minima is

A convex lens of focal length $20 cm$ produces images of the same magnification 2 when an object is kept at two distances ${x}_{1}$ and ${x}_{2}({x}_{1}>{x}_{2})$ from the lens. The ratio of ${x}_{1}$ and ${x}_{2}$ is:

What is the position and nature of image formed by lens combination shown in figure? ( ${f}_{1}, {f}_{2}$ are focal lengths) 

The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following graphs is the correct one, if $D_{m}$ is the angle of minimum deviation? 

A convex lens is put $10 cm$ from a light source and it makes a sharp image on a screen, kept $10 cm$ from the lens. Now a glass block (refractive index 1.5) of $1.5 cm$ thickness is placed in between the light source and the lens. To get the sharp image again, the screen is shifted by a distance $d.$ Then $d$ is: 

The figure shows a Young's double slit experimental setup. It is observed that when a thin transparent sheet of thickness t and refractive index $\mu$ is put in front of one of the slits, the central maximum gets shifted by a distance equal to n fringe width. If the wavelength of light used is $\lambda$ then $t$ will be: 

In an interference experiment the ratio of amplitudes of coherent waves is $\frac{{a}_{1}}{{a}_{2}}=\frac{1}{3}$ . The ratio of maximum and minimum intensities of fringes will be:

In a Young's double slit experiment slit separation $0.1 mm,$ one observes a bright fringe at angle $\frac{1}{40} rad$ by using light of wavelength ${\lambda }_{1}.$ When the light of wavelength ${\lambda }_{2}$ is used a bright fringe is seen at the same angle in the same set up. Given that ${\lambda }_{1}$ and ${\lambda }_{2}$ are in visible range $(380 nm to 740 nm),$ their values are:

Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror $({M}_{1})$ and parallel to the second mirror $({M}_{2})$ is finally reflected from the second mirror $({M}_{2})$ and parallel to the first mirror $({M}_{1}).$ The angle between the two mirrors will be:

Consider a tank made of glass (refractive index $1.5$ ) with a thick bottom. It is filled with a liquid of refractive index $\mu .$ A student finds that, irrespective of what the incident angle $i$ (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of $\mu$ is: 

Formation of real image using a biconvex lens is shown below:  If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?

A ray of light $AO$ in vacuum is incident on a glass slab at angle $60^{\circ}$ and refracted at angle $30^{\circ}$ along $OB$ as shown in the figure. The optical path length of light ray from $A$ to $B$ is: