Optical Path Length

Q.

On introducing a thin film in the path of one of the two interfering beams, the central fringe will shift by one fringe width. If $\mu =1.5$, the thickness of the film is (wavelength of monochromatic light is $\lambda$)

1. $4\lambda$

2. $3\lambda$

3. $2\lambda$

4. $\lambda$

Q. When a mica sheet of thickness 7 microns and $\mu =1.6$ is placed in the path of one of interfering beams in the $YDSE$, then the central fringe gets at the position of the seventh bright fringe. What is the wavelength of light used ?

1. $6000\stackrel{\circ }{A}$
2. $3000\stackrel{\circ }{A}$
3. $4000\stackrel{\circ }{A}$
4. $2000\stackrel{\circ }{A}$

Q.

Monochromatic light of wavelength of 600nm is used in a YDSE. One of the slits is covered by a transparent sheet of thickness $1.8\times {10}^{-5}m$ made of a material of refractive index 1.6. How many fringes will shift due to the introduction of the sheet?

1. 18

2. 12

3. 20

4. 10

Q.

In the ideal double-slit experiment, when a glass-plate (refractive index 1.5) of thickness t is introduced in the path of one of the interfering beams (wavelength l), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is

[IIT-JEE (Screening) 2002]

1. 2l

2. 
   

3. 
   

4. l

Q. In a YDSE, light of wavelength $\lambda =5000\stackrel{\circ }{A}$ is used, which emerges in phase from two slits a distance $d=3\times {10}^{-7}m$ apart. A transparent sheet of thickness $t=1.5\times {10}^{-7}m$, refractive index $n=1.17$, is placed over one of the slits. Where does the central maxima of the interference now appear from the center of the screen? (Find the value of y?)

1. $\frac{D(\mu -1)t}{2d}$
2. $\frac{2D(\mu -1)t}{d}$
3. $\frac{D(\mu +1)t}{d}$
4. $\frac{D(\mu -1)t}{d}$

Q. An electromagnetic wave of wavelength ${\lambda }_0$ (in vacuum) passes from $P$ towards $Q$ crossing three different media of refractive index $\mu ,2\mu$ and $3\mu$ respectively as shown in figure. ${\varphi }_P$ and ${\varphi }_Q$ are the phase of the wave at point $P$ and $Q$. Find the phase difference ${\varphi }_Q-{\varphi }_P$ [Take: $\mu =1$]

1. $0$
2. $\frac{\pi }{4}$
3. $\frac{\pi }{2}$
4. $\pi$

Q. In a Young's double slit experiment, the fringes are displaced by a distance $x$ when a glass plate of refractive index $1.5$ is introduced in the path of one of the beams. When this plate is replaced by another plate of same thickness, the shift of fringes is $\left(3/2\right)x$. The refractive index of second plate is

1. $1.75$
2. $1.40$
3. $1.25$
4. $1.67$

Q. A glass of thickness 1 micron is placed in the path of one of the interfering beams in a YDSE experiment. If the wavelength of the source is $6000\dot{A}$ and the central band is found to shift by one band width, find the refractive index of glass.

1. 1.1
2. 1.3
3. 1.4
4. 1.6

Q. There is an equilateral prism of refractive index 3 on which a light ray is incident normally on one face as shown in the figure. Find the length of the path travelled by the light ray inside the prism.

1. $\sqrt{3}\frac{L}{2}$
2. $\sqrt{3}L$
3. $\frac{3L}{2}$
4. L

Q. A narrow monochromatic beam of light of intensity I is incident on a glass plate as shown in figure. Another identical glass plate is kept close to the first one and parallel to it. Each glass plate reflects $25\%$ of the light incident on it and transmits the remaining. Find the ratio of minimum and maximum intensities in the interference pattern formed by two beams obtained after one reflection at each plate.

Q. A plate of thickness t made of a material of refractive index $\mu$ is placed in front of one of the slits in a double-slit experiment. What should be the minimum thickness t which will make the intensity at the centre of the fringe pattern zero?

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

Q. A beam of light has frequency of $5\times {10}^{14}Hz$. How many wavelengths of this light wave are there in 0.1 mm thick glass tape $(n_{glass}=1.5)$?

1. 100
2. 150
3. 250
4. 300

Q. In the ideal double – slit experiment, when a glass – plate $(\mu =1.5)$ of thickness t is introduced in the path of one of the interfering beams $(wave–length\lambda )$, the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass – plate is

1. $2\lambda$
2. $\frac{2\lambda }{3}$
3. $\frac{\lambda }{3}$
4. $\lambda$

Q. A thin film of soap solution of refractive index $\mu$ and thickness t appears shining by a normal reflected light wavelength $\lambda$ then t can be

1. $\frac{\lambda }{2\mu }$
2. $\frac{2\lambda }{3\mu }$
3. $\frac{3\lambda }{8\mu }$
4. $\frac{6\lambda }{8\mu }$

Q. Young’s double slit experiment is carried with two thin sheets of thickness $10.4\mu m$ each and refractive index ${\mu }_1=1.52$ and ${\mu }_2=1.40$ covering the slits $S_1$ and $S_2$, respectively, If white light of range 400 nm to 780 nm is used, then which wavelength will form maxima exactly at point O, the centre of the screen?

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