Variable Refractive Index

Q. A light beam is travelling from Region I to Region IV (refer figure). The refractive index in Region I, II, III and IV are $n_0,\frac{n_0}{2},\frac{n_0}{6}and\frac{n_0}{8}$ respectively. The angle of incidence $\theta$ for which the beam just misses entering Region IV is

(IIT-JEE 2008)

1. $si{n}^{-1}\left(\frac{3}{4}\right)$
2. $si{n}^{-1}\left(\frac{1}{8}\right)$
3. $si{n}^{-1}\left(\frac{1}{4}\right)$
4. $si{n}^{-1}\left(\frac{1}{3}\right)$

Q. A system of coordinates is drawn in a medium whose refractive index varies as $\mu =\frac{2}{1+y^2}$, where $0\le y\le 1$ and $\mu =2$ for $y<0$ as shown in figure. A ray of light is incident at origin at an angle ${60}^{\circ }$ with y - axis as shown in the figure. At point $P$, ray becomes parallel to x - axis. The value of $H$ is:-

1. ${(\frac{2}{\sqrt{3}}-1)}^{\frac{1}{2}}$
2. ${\left(\frac{2}{\sqrt{3}}\right)}^{\frac{1}{2}}$
3. ${(\sqrt{3}-1)}^{\frac{1}{2}}$
4. ${(\frac{4}{\sqrt{3}}-1)}^{\frac{1}{2}}$

Q. A ray of light parallel to $x-$axis is incident on a circle $x^2+y^2=R^2$ polished from inside as shown in the figure. Find the co-ordinate of $x\text{and}y$ of the point at which the incident ray should fall such that the reflected ray deviated by ${60}^{\circ }$ after reflection.

1. $(x,y)=(\frac{\sqrt{3}R}{2},-\frac{R}{2})$
2. $(x,y)=(\frac{R}{\sqrt{2}},-\frac{R}{2})$
3. $(x,y)=(-\frac{R}{2},\frac{\sqrt{3}R}{2})$
4. $(x,y)=(-\frac{R}{\sqrt{2}},\frac{R}{\sqrt{2}})$

Q. Match the proper entries from column- II to column-I using the codes given below in the columns. Deviation given in column-II is the magnitude of total deviation (between incident ray and finally refracted or reflected ray) which lies between $0^{\circ }$ and ${180}^{\circ }.$ Here $n$ represents refractive index of medium.

Column-I	Column-II
(p)	(1) deviation in the light ray is greater than ${90}^{\circ }$
(q)	(2) deviation in the light ray is less than ${60}^{\circ }$
(r)	(3) deviation in the light ray is greater than ${60}^{\circ }$ but less than or equal to ${90}^0$
(s)	(4) speed of light remains same after falling on the boundary of two mediums.

1. p-4, 2; q-2, 4; r-1, 4; s-3
2. p-1, 4; q-2; r-3, 4; s-3
3. p-1, 4; q-3; r-3, 4; s-3
4. p-3, 4; q-1, 4; r-4; s-2

Q. The condition for obtaining secondary maxima in the diffraction pattern due to single slit is :

1. $a\sin \theta =\frac{n\lambda }{2}$
2. $a\sin \theta =(2n-1)\lambda /2$
3. $a\sin \theta =n\lambda$
4. $a\sin \theta =(2n-1)\lambda$

Q. A spherical surface of radius of curvature 10 cm separates two media X and Y of refractive indices 3/2 and 4/3 respectively. Centre of the spherical surface lies in denser medium. An object is placed in medium X. For image to be real, the object distance must be

1. greater than 80 cm
2. less than 80 cm
3. greater than 90 cm
4. less than 90 cm

Q. In YDSE, if the thickness of a glass slab $(\mu =1.5)$ which should be placed before the upper slit $S1$ so that the central maximum now lies at a point where 5th bright fringe was lying earlier (before inserting the slab) is $Y\ast 10,000\mathring{A}$. (Wavelength of light used is $5000\mathring{A}$.) Find Y?

Q.

A ray light is incident at the glass-water interface at an angle i, it merges finally parallel to the surface of water, then the value of ${\mu }_g$ would be

1. (4/3) sin i

2. 1 /sin i

3. 4/3

4. 1

Q. A ray of light travelling in air has wavelength $\lambda$, frequency $n$, velocity $v$ and intensity $I$. If this ray enters into water then these parameters are ${\lambda }^{\prime },n^{\prime },v^{\prime }{I}^{\prime }$ respectively.

1. $\lambda =\lambda$
2. $n=n^{\prime }$
3. $I=I^{\prime }$
4. $v=v^{\prime }$

Q. The fringe width $\beta$ of the fringes produced in Young's double slit experiment conducted for monochromatic light of wavelength $\lambda$ with slit difference $d$ and separation between slits and screen $D$ is :

1. $\beta =\frac{\lambda D}{d}$
2. $\beta =\frac{Dd}{\lambda }$
3. $\beta =\frac{\lambda d}{D}$
4. $\beta =\frac{\lambda d^2}{D^2}$

Q. An air bubble inside a water tank would behave as a

1. Concave lens
2. Convex lens
3. May be both
4. Neither concave, nor convex lens

Q. The condition for obtaining secondary maxima in the diffraction pattern due to single slit is (symbols have their usual meaning)

1. a sin $\theta$ = n$\lambda$
2. a sin $\theta$ = (2n - 1) $\frac{\lambda }{2}$
3. a sin $\theta$ = $\frac{n\lambda }{2}$
4. a sin $\theta$ = (2n - 1) $\lambda$

Q. When light rays approach the slits as shown in the figure below making an angle $\theta$ with the central axis, the number of maxima lying between $O$ and the central maxima will be :

1. $\frac{d\sin \theta }{\lambda }$
2. $\frac{d\sin \theta }{\lambda }-1$
3. $\frac{yD}{d}$
4. $\frac{d\sin \theta }{2\lambda }$

Q. If YDSE is immersed in a liquid of refractive index ${}^{\prime }\mu {}^{\prime }$ then the fringe width ${}^{\prime }\beta {}^{\prime }$

1. decreases by $\mu$
2. increases by $\mu$
3. remains unchanged
4. none of these

Q. Suppose a star which is 100 light years away explodes today.It is highly unlikely that you will be able to see the explosion. Why?

Q. Young's double slit experiment is carried with two sheets of thickness 10.4 $\mu a$ each and refractive index $\mu =1.52and{\mu }_2=1.40$ covering the slits $s_{1}and{s}_2$ respectively. If while light of range 400 nm to 780 nm is used then which wavelength will from maximum exactly at pointO the center of the screen?

1. 416 nm only
2. 624 nm only
3. 416 nm and 624 nm only
4. none of these

Q. Angle made by light ray with the normal in medium of refractive index $\sqrt{2}$ is

1. ${\sin }^{-1}\sqrt{\frac{3}{8}}$
2. ${\sin }^{-1}\sqrt{\frac{3}{6}}$
3. ${\sin }^{-1}\sqrt{\frac{3}{10}}$
4. ${\sin }^{-1}\sqrt{\frac{3}{4}}$

Q.

A ray light is incident at the glass-water interface at an angle i, it merges finally parallel to the surface of water, then the value of ${\mu }_g$ would be

1. (4/3) sin i

2. 1 /sin i

3. 4/3

4. 1

Q. The condition for obtaining secondary maxima in the diffraction pattern due to single slit is

1. $a\sin \theta =n\lambda$
2. $a\sin \theta =(2n-1)\frac{\lambda }{2}$
3. $a\sin \theta =(2n-1)\lambda$
4. $a\sin \theta =\frac{n\lambda }{2}$

Q. A material having an index of refraction $n$ is surrounded by vacuum and is in the shape of a quarter circle of radius $R$ (Fig. $P35.71$ ). A light ray parallel to the base of the material is incident from the left at a distance $L$ above the base and emerges from the material at the angle $\theta$. Determine an expression for $\theta$ in terms of $n,R,$ and $L$

Q. The refractive index of a medium is $\sqrt{3}$. If the unpolarized light is incident on it at the polarizing angle of the medium, the angle of refraction is:

1. $0^{\circ }$
2. ${60}^{\circ }$
3. ${45}^{\circ }$
4. ${30}^{\circ }$

Q. When the light ray illustrated in this Figure passes through the glass block of the index of refraction $n=1.50$, it is shifted laterally by the distance $d$.
Find the time interval required for the light to pass through the glass block.

Q. Monochromatic green light, of wavelength $550nm,$ illuminates two parallel narrow slits $7.70\mu m$ apart. Calculate the angular deviation of the third-order $(m=3)$ bright fringe in radians.

Q. A ray of light travelling along the line $x+y=1$ is inclined on the $x$-axis and after refraction it enters the other side of the $x$-axis by turning ${15}^{\circ }$ away from the $x$-axis. The equation of the line along which the refraction ray travels is

1. $\sqrt{3}y-x+1=0$
2. $\sqrt{3}y+x+1=0$
3. $\sqrt{3}y+x-1=0$
4. None of these

Q. Find the distance of object placed in the slab of refractive index $\mu$ from point P of the curved surface of radius R so that image is formed at infinity

1. $\frac{(\mu -1)R}{\mu }$
2. $\frac{\mu R}{(\mu -1)}$
3. $\frac{(\mu -1)R}{2\mu }$
4. $\frac{R}{(\mu -1)}$