Question 27: Wave Optics

Question

In Young's double slit experiment light of wavelength $$500 \mathrm{~nm}$$ is used to form interference pattern. A uniform glass plate of refractive index 1.5 and thickness $$0.1 \mathrm{~mm}$$ is introduced in the path of one of the interfering beams. The number of fringes that will shift due to this is

Accepted Answer

YoungÃ¢ÂÂs double slit experiment involves the interference of light waves originating from two slits which produce a pattern of bright and dark fringes due to constructive and destructive interference respectively. In this problem, we introduce a glass plate in the path of one of the beams, which causes an additional path difference due to the change in the optical path length.
Given:
Wavelength of light, $$\lambda = 500 \ \mathrm{nm} = 500 	imes 10^{-9} \ \mathrm{m}$$
Refractive index of the glass plate, $$n = 1.5$$
Thickness of the glass plate, $$t = 0.1 \ \mathrm{mm} = 0.1 	imes 10^{-3} \ \mathrm{m}$$
The optical path difference introduced by the glass plate is given by:
$$\Delta d = (n - 1) t$$
Substituting the given values:
$$\Delta d = (1.5 - 1) 	imes 0.1 	imes 10^{-3} \ \mathrm{m} = 0.5 	imes 0.1 	imes 10^{-3} \ \mathrm{m} = 0.05 	imes 10^{-3} \ \mathrm{m} = 5 	imes 10^{-5} \ \mathrm{m}$$
The shift in the number of fringes due to this path difference is given by:
$$	ext{Number of fringes} = \frac{\Delta d}{\lambda}$$
Substituting the values for $$\Delta d$$ and $$\lambda$$:
$$	ext{Number of fringes} = \frac{5 	imes 10^{-5} \ \mathrm{m}}{500 	imes 10^{-9} \ \mathrm{m}} = \frac{5 	imes 10^{-5}}{500 	imes 10^{-9}} = \frac{5 	imes 10^{-5}}{5 	imes 10^{-7}} = \frac{1}{10^{-2}} = 100$$
Thus, the number of fringes that will shift due to the introduction of the glass plate is 100.
The correct option is
A. 100

Answer

100

Answer

400

Answer

300

Answer

200

Wave Optics

In Young's double slit experiment light of wavelength $500 \mathrm{~nm} is used to form interference pattern. A uniform glass plate of refractive index 1.5 and thickness 0.1 \mathrm{~mm}$ is introduced in the path of one of the interfering beams. The number of fringes that will shift due to this is

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