Question

: A laser beam is incident on two slits with separation d-0.038 mm. A screen is placed L-1.6 m from the slits. The wavelength of the laser light is A 4750 Å. and θ2 are the angles to the first and second bright fringes above the center of the screen. Otheex ee 25% Part (a) Express sin(91) in terms of d and λ. sin(θ 1) Add V Correct! 25% Part (b) Express sin(92) in terms of d and λ. sin(02) (2 A )yd Correct 25% Part (c) Express the distance between the two bright fringes on the screen, y, in terms of θ1, θ2 and L. Grade S Deductic Potentia 9 cotan(0) cotan(02) in(a)N 4 5 6 cos(0) | (.ilM-17 8 cos(α) cos(φ) Submiss Attempts per detailed sin(φ) tan(6) sin(0) tan(01) Hint I give up! Submit Feedback: deduction per feedback Hints: 0%, deduction per hint. Hints remaining: 2 25% Part (d) Solve for the numerical value of y ¡n meters.

Answer 1

Answer:

Explanation:

Distance between two slits d = .038 x 10⁻³m

Distance of screen L = 1.6 m

Wave-length of light λ = 4750 x 10⁻¹⁰ m

If x₁ be the position of first bright fringe on the screen

Sinθ₁ =  x₁ / L

For position of second bright fringe

Sinθ₂ =  x₂ / L

Again, for the formation of first bright fringe

a ) path difference = λ

x₁ d / L = λ

d Sinθ₁ = λ

Sinθ₁ = λ / d

b ) Similarly for second bright fringe

Sinθ₂ = 2 λ / d

c ) Distance between two bright fringes

x₂ - x₁ = y

y = L ( Sinθ₂ - Sinθ₁ )

d )

y = L ( Sinθ₂ - Sinθ₁ )

=  L ( 2 λ / d -  λ / d )

= Lλ / d

= $\frac{1.6\times4750\times10^{-10}}{.038\times10^{-3}}$

= 2 x 10⁻² m

= 2 cm .