Optical Path Length

Q. Find the formula for maximum minima and maxima which can be obtained on the screen in single slit diffraction and in ydse

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. A glass surface is coated by an oil film of uniform thickness 1.00 × 10⁻⁴ cm. The index of refraction of the oil is 1.25 and that of the glass is 1.50. Find the wavelengths of light in the visible region (400 nm − 750 nm) which are completely transmitted by the oil film under normal incidence.

Q. In YSDE the intensity of light at a point on the screen where the path difference is lambda is I. The intensity of light at a point where the path difference becomes lambda/3 is

Q. Light of wavelength $6000\stackrel{\circ }{A}$ is incident along the normal on a glass plate of refractive index 1.5. What should be the smallest thickness of the plate which will make it appear darker when reflection is observed ?

1. $6000\stackrel{\circ }{A}$
2. $5000\stackrel{\circ }{A}$
3. $3000\stackrel{\circ }{A}$
4. $2000\stackrel{\circ }{A}$

Q. Of the two slits producing interference in Young’s experiment, one is covered with glass so that light intensity passing is reduced to 50%. Which of the following is correct?

1. Intensity of fringes remains unaltered
2. Intensity of bright fringe decreases and that of dark fringe increases
3. Intensity of bright fringe increases and that of dark fringe decreases
4. Intensity of both bright and dark fringes decreases

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 plate of thickness t made of a material of refractive index µ is placed in front of one of the slits in a double slit experiment. (a) Find the change in the optical path due to introduction of the plate. (b) What should be the minimum thickness t which will make the intensity at the centre of the fringe pattern zero? Wavelength of the light used is $\lambda$. Neglect any absorption of light in the plate.

Q. A thin film $(\mu =1.6)$ of thickness ${10}^{-3}$ mm is introduced in the path of the one of the two interfering beams. The central fringe moves to a position occupied by the ${10}^{th}$ bright fringe earlier. The wavelength of light is:

1. $600\dot{A}$
2. $6000\dot{A}$
3. $60\dot{A}$
4. $660\dot{A}$

Q. A transparent paper (refractive index = 1⋅45) of thickness 0⋅02 mm is pasted on one of the slits of a Young's double slit experiment which uses monochromatic light of wavelength 620 nm. How many fringes will cross through the centre if the paper is removed?

Q. A double slit experiment is performed with light of wavelength 500 nm. A thin film of thickness 2$\mu$ m and refractive index 1.5 is introduced in the path of the upper beam. The location of the central maximum will:

1. Remain unshifted
2. Shift downward by nearly two fringes
3. Shift upward by nearly two fringes
4. Shift downward by 10 fringes

Q. An optical fibre (μ = 1.72) is surrounded by a glass coating (μ = 1.50). Find the critical angle for total internal reflection at the fibre-glass interface.

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. 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 (wavelength $\lambda$), the intensity at the position where central maxima occurred previously remains unchanged. The minimum thickness of glass plate is $k\lambda$, then the value of $k$ is (Integer only)

Q. If we observe the single slit Fraunhofer diffraction with wavelength $\lambda$ and slit width $b$, the angular width $\left({\theta }_w\right)$ of the central maxima is $2\theta$. On decreasing the slit width for the same $\lambda$

1. $\theta$ remains inchanged
2. $\theta$ increases
3. $\theta$ increases or decreases depending on the intensity of light
4. $\theta$ decreases

Q. Can central fringe width be smaller than length of slit in single slit diffraction pattern?

Q. A thin film $(\mu =1.6)$ of thickness ${10}^{-3}$ mm is introduced in the path of the one of the two interfering beams. The central fringe moves to a position occupied by the ${10}^{th}$ bright fringe earlier. The wavelength of light is:

1. $600\dot{A}$
2. $6000\dot{A}$
3. $60\dot{A}$
4. $660\dot{A}$

Q. A transparent film of thickness $5\mu \text{m}$ and refractive index $1.4$ is placed in front of the lower slit as shown in the diagram. As a result, the interference pattern shifts through a distance $2\text{mm}$. Find the order of the bright/dark band forming at point $O$ after placing the film. The wavelength of the monochromatic light used is $5000\mathring{\text{A}}$.

1. Fourth dark fringe
2. Second bright fringe
3. Fourth bright fringe
4. Second dark fringe

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. 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. 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

Q. Find the thickness of a plate which will produce a change in optical path equal to half the wavelength λ of the light passing through it normally. The refractive index of the plate is μ.

Q. A mica strip and a polystyrene strip are fitted on the two slits of a double slit apparatus. The thickness of the strips is 0⋅50 mm and the separation between the slits is 0⋅12 cm. The refractive index of mica and polystyrene are 1.58 and 1.55, respectively, for the light of wavelength 590 nm which is used in the experiment. The interference is observed on a screen at a distance one metre away. (a) What would be the fringe-width? (b) At what distance from the centre will the first maximum be located?