Optics PYQ — Page 13

In Young's double slit arrangement, slits are separated by a gap of $0.5\mathrm{mm}$, and the screen is placed at a distance of $0.5m$ from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of $5890\overset{o}{A}$ is :-

A short straight object of height $100\mathrm{cm}$ lies before the central axis of a spherical mirror whose focal length has absolute value $|f|=40\mathrm{cm}$. The image of object produced by the mirror is of height $25\mathrm{cm}$ and has the same orientation of the object. One may conclude from the information:

Region $I$ and $\mathrm{II}$ are separated by a spherical surface of radius $25\mathrm{cm}$. An object is kept in region $I$ at a distance of $40\mathrm{cm}$ from the surface. The distance of the image from the surface is: 

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is _____ $\mathrm{mm}$. [Refractive index of air $=1.0003$, the wavelength of yellow light in vacuum $=6000\overset{\circ }{A}]$

The same size images are formed by a convex lens when the object is placed at $20\mathrm{cm}$ or at $10\mathrm{cm}$ from the lens. The focal length of convex lens is

A fringe width of $6\mathrm{mm}$ was produced for two slits separated by $1\mathrm{mm}$ apart. The screen is placed $10m$ away. The wavelength of light used is $x$ $\mathrm{nm}$. The value of $x$ to the nearest integer is ______.

The angle of deviation through a prism is minimum when  (A) Incident ray and emergent ray are symmetric to the prism (B) The refracted ray inside the prism becomes parallel to its base (C) Angle of incidence is equal to that of the angle of emergence (D) When angle of emergence is double the angle of incidence Choose the correct answer from the options given below :

An object is placed beyond the centre of curvature $C$ of the given concave mirror. If the distance of the object is ${d}_{1}$ from $C$ and the distance of the image formed is ${d}_{2}$ from $C,$ the radius of curvature of this mirror is:

A source of light is placed in front of a screen. The intensity of light on the screen is $I$. Two Polaroids ${P}_{1}$ and ${P}_{2}$ are so placed in between the source of light and screen that the intensity of light on the screen is $\frac{I}{2}$. Then the ${P}_{2}$, should be rotated by an angle of (degrees) so that the intensity of light on the screen becomes $\frac{3I}{8}$.

Your friend is having eye sight problem. She is not able to see clearly a distant uniform window mesh and it appears to her as nonuniform and distorted. The doctor diagnosed the problem as :

An object viewed from a near point distance of $25\mathrm{cm}$, using a microscopic lens with magnification $6,$ gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length $0.6m$, if the focal length of the eyepiece is equal to ____ $\mathrm{cm}.$

The refractive index of a converging lens is $1.4$. What will be the focal length of this lens if it is placed in a medium of same refractive index ? (Assume the radii of curvature of the faces of lens are ${R}_{1}$ and ${R}_{2}$ respectively)

The expected graphical representation of the variation of angle of deviation ' $\delta$ ' with angle of incidence 'i' in a prism is :

White light is passed through a double slit and interference is observed on a screen $1.5m$ away. The separation between the slits is $0.3\mathrm{mm}$. The first violet and red fringes are formed $2.0\mathrm{mm}$ and $3.5\mathrm{mm}$ away from the central white fringes. The difference in wavelengths of red and violet light is $(\text{in}\mathrm{nm}).$

Curved surfaces of a plano-convex lens of refractive index ${\mu }_{1}$ and a plano-concave lens of refractive index ${\mu }_{2}$ have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses 

A ray of light entering from air into a denser medium of refractive index $\frac{4}{3}$, as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle $\theta$ should be equal to: 

A point source of light $S$, placed at a distance $60\mathrm{cm}$ infront of the centre of a plane mirror of width $50\mathrm{cm}$, hangs vertically on a wall. A man walks infront of the mirror along a line parallel to the mirror at a distance $1.2m$ from it (see in the figure). The distance between the extreme points where he can see the image of the light source in the mirror is__$\mathrm{cm}$ 

The incident ray, reflected ray and the outward drawn normal are denoted by the unitvectors $\vec{a},\vec{b}$and $\vec{c}$ respectively. Then choose the correct relation for these vectors.

In a Young's double slit experiment two slits are separated by $2\mathrm{mm}$ and the screen is placed one meter away. When a light of wavelength $500\mathrm{nm}$ is used, the fringe separation will be :

A ray of light passes from a denser medium to a rarer medium at an angle of incidence $i.$ The reflected and refracted rays make an angle of $90^{\circ}$ with each other. The angle of reflection and refraction are respectively $r$ and ${r}^{'}.$ The critical angle is given by, 

The refractive index of a medium where speed of light is 2 × 10⁸ m/s is:

In a Young's double slit experiment, light of $500\mathrm{nm}$ is used to produce and interference pattern. When the distance between the slits is $0.05\mathrm{mm},$ the angular width (in degree) of the fringes formed on the distance screen is close to :

Orange light of wavelength $6000\times {10}^{–10}m$ illuminates a single slit of width $0.6\times {10}^{–4}m$. The maximum possible number of diffraction minima produced on both sides of the central maximum is __________

A Young's double-slit experiment is performed using monochromatic light of wavelength $\lambda$. The intensity of light at a point on the screen, where the path difference is $\lambda$, is $K$ units. The intensity of light at a point where the path difference is $\frac{\lambda }{6}$ is given by $\frac{\mathrm{nK}}{12}$, where $n$ is an integer. The value of $n$ is