Two slits are one millimeter apart and the screen is placed one metre away. The wavelength of light used is 500 nm What should be the width of each slit to obtain 10 maxima of the double-slit pattern within the central maxima of the single slit pattern.

Question

Two slits are one millimeter apart and the screen is placed one metre away. The wavelength of light used is 500 nm What should be the width of each slit to obtain 10 maxima of the double-slit pattern within the central maxima of the single slit pattern. (A) 0.1 mm (B) 0.2 mm (C) 0.4 mm (D) 0.5 mm

Tardigrade Admin · Accepted Answer

Width of central maxima in diffraction =(2 D λ/a) Width of 10 interference fringes =10((D λ/d)) ⇒ (10 D λ/d)=(2 D λ/a) or a=(d/5)=(1 mm /5)=0.2 mm

Q. Two slits are one millimeter apart and the screen is placed one metre away. The wavelength of light used is 500 nm What should be the width of each slit to obtain 10 maxima of the double-slit pattern within the central maxima of the single slit pattern.

0.1 mm

0.2 mm

0.4 mm

0.5 mm

Width of central maxima in diffraction $= \frac{2 D λ}{a}$
Width of 10 interference fringes $= 10 (\frac{D λ}{d})$
$\Rightarrow \frac{10 D λ}{d} = \frac{2 D λ}{a}$
or $a = \frac{d}{5} = \frac{1 mm}{5} = 0.2 mm$

Q. Two slits are one millimeter apart and the screen is placed one metre away. The wavelength of light used is 500 nm What should be the width of each slit to obtain 10 maxima of the double-slit pattern within the central maxima of the single slit pattern.

0.1 mm

0.2 mm

0.4 mm

0.5 mm

Width of central maxima in diffraction =a2Dλ​ Width of 10 interference fringes =10(dDλ​) ⇒d10Dλ​=a2Dλ​ or a=5d​=51mm​=0.2mm

Width of central maxima in diffraction $= \frac{2 D λ}{a}$
Width of 10 interference fringes $= 10 (\frac{D λ}{d})$
$\Rightarrow \frac{10 D λ}{d} = \frac{2 D λ}{a}$
or $a = \frac{d}{5} = \frac{1 mm}{5} = 0.2 mm$