Wave Optics Test

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The YDSE apparatus is modified by placing an isotropic transparent plate of high melting point in front of one of the slits. The refractive index of the plate is $$\mu_{r} =1.5$$ at room temperature and its thickness is $$t = 2\mu m$$. The refractive index of plate will increase when temperature increases and temperature coefficient of refractive index of the plate (i.e., the fractional change in refractive index per unit rise in temperature) is $$2\times 10^{-6}/ ^{\circ}C$$. The incident light is having wavelength $$\lambda = 600\overset {\circ}{A}$$. The separation between the slits is $$d = 0.2\ cm$$, and separation between the slit and the screen is $$2\ m$$. Assume that slits are of equal intensity.
Based on the above information, answer the following questions:

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If the plate is heated so that it temperature rises by $$10^{\circ}C$$, then how many fringes will cross a particular point on the screen? (Neglect the thermal expansion of plate):

Wave Optics Tes...

Question 1

$$(\mu - 1)t = d\sin \theta$$

$$(\mu - 1) t = d\cos \theta$$

$$(\mu - 1)t + d\sin \theta = 0$$

$$\dfrac {t}{\mu - 1} = \dfrac {d}{\sin \theta}$$

Question 2

$$1000$$

$$10^{-4}$$

$$5000$$

$$\dfrac {1}{3000}$$

Question 3

fringe pattern disappears

bright fringes become brighten and dark one becomes darker

dark and bright fringes get fainter

dark fringes get brighter and bright fringes get darker

Question 4

$$\dfrac{I_{0}}{2}$$

$$\dfrac{3}{4}I_{0}$$

$$I_{0}$$

$$\dfrac{I_{0}}{4}$$

Question 5

$$2$$

$$4$$

$$6$$

$$8$$

Question 6

$$4I_{0}$$

$$2I_{0}$$

$$3I_{0}$$

$$\dfrac {7}{2}I_{0}$$

Question 7

$$0.853$$

$$8.53$$

$$0.75$$

$$7.5$$

Question 8

$$\left({\lambda_{1}+\lambda_{2}}{2D}\right)d$$

$$\dfrac{\lambda_{1}-\lambda_{2}}{2D} \times 2d$$

LCM of $$\dfrac{\lambda_{1}D}{d}$$ and $$\dfrac{\lambda_{2}D}{d}$$

HCF of $$\dfrac{\lambda_{1}D}{d}$$ and $$\dfrac{\lambda_{2}D}{d}$$

Question 9

$$\dfrac{2\mu \sin \theta }{1.22\lambda}$$

$$\dfrac{\mu \sin \theta }{1\lambda}$$

$$\dfrac{2\mu \cos \theta }{1.22}$$

$$\dfrac{2\mu }{\lambda}$$

Question 10

Vertically downward slightly

Vertically upwards slightly

Horizontally, slightly to the left

Horizontally, slightly to the right

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