Question

Light of wavelength 6×10^(-5) cm falls on a narrow slit.The pattern formed is observed on a screen placed on a screen placed at a distance of 90 cm from the slit.Calculate the width of the slit if the 1st minima lies 0.09mm on the other side of the central maximum.​

Answer 1

Answer:

=> SLIT WIDTH ( d ) = 3 mm (OR) [ 30 cm ]

Explanation:

★ WAVE OPTICS ★

★ GIVEN ;

» Wavelength ( lambda ) = 6 × 10^-7 m

» Distance of Screen from Slit ( D ) = 90 cm

» Order of Fringe ( n ) = 1st Minima

» Position of Destructive Interference

( Y ) = 0.09 mm

★ SLIT WIDTH ( d ) = ???

______ [ BY USING FORMULA ] _____

$[Y \: = \: ( \: \frac{( \: 2n \: - \: 1 \: ) \: \times \: Wavelength \: (lambda) \: \times \: D \: \: }{ \: 2 \: \times \: Slit \: Width \: (d) \: } ) ]$

★ Y = [ ( 2n -1 ) × Lambda × D ] / 2d

» d = [ ( 2n-1 ) × Lambda × D ] / 2 × Y

» d = [ ( 2n - 1 ) × 6 × 10^-7 × 0.9 ] / 2 × 9 × 10^-5 m

» d = [ ( 2(1) - 1 ) × 54 × 10^-8 ] / 18 × 10^-5

» d = [ 1 × 54 × 10^-8 ] / 18 × 10^-5

» d = 3 × 10^-8 / 10^-5

★ SLIT WIDTH ( d ) = 3 × 10-³ m

–––––––––– [ OR ] –––––––––

★ SLIT WIDTH ( d ) = 3 mm

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ANSWER :- SLIT WIDTH IN YDSE OF DESTRUCTIVE INTERFERENCE IS ;

[ d = 3 Millimeters ]