Geometrical OpticsHard
Question
In a Young′s double slit experiment, 12 fringes are observed to be formed in a certain segment of the screen when light of wavelength 600 nm is used. If the wavelength of light is changed to 400 nm, number of fringes observed in the same segments of the screen is given by
Options
A.12
B.18
C.24
D.30
Solution
Fringe width, 
When the wavelength is decreased from 600 nm to 400 nm, fringe width will also decrease by a factor of
or 
or the number of fringes in the same segment will increase by a factor of 3/2.
Therefore, number of fringes observedin the same segment = 12 ×
= 18.
Note : Since ω ∝ λ, therefore, if YDSE apparatus is immersed in a liquid of refractive index, the wavelength λ and thus the fringe width will decrease μ times.
When the wavelength is decreased from 600 nm to 400 nm, fringe width will also decrease by a factor of
or or the number of fringes in the same segment will increase by a factor of 3/2.Therefore, number of fringes observedin the same segment = 12 ×
= 18. Note : Since ω ∝ λ, therefore, if YDSE apparatus is immersed in a liquid of refractive index, the wavelength λ and thus the fringe width will decrease μ times.
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