Question

A parallel beam of light of wavelength 6000 A.U. is incident normally on a narrow slit of width 0.2 mm. The angular separation between first and second minima is
a) 0.003 rad
b) 0.006 rad
c) 0.5 degree
d) 0.3 degree​

Answer 1

Answer:

• The angular separation is 0.003

Explanation:

Given,

λ = 6000 Å = 6000 × 10⁻¹⁰ = 6 × 10⁻⁷ m.

d = 0.2mm = 0.2 × 10⁻³ = 2 × 10⁻⁴ m.

For first minima,

⇒ d sinθ = λ

Substituting the values,

⇒ 2 × 10⁻⁴ × sinθ = 6 × 10⁻⁷

⇒ sinθ = 6 × 10⁻⁷/2 × 10⁻⁴

⇒ sinθ = 3 × 10⁽⁻⁷⁺⁴⁾

⇒ sinθ = 3 × 10⁻³

⇒ sinθ = 0.003

(Sinθ value is so small that it nearly equals the value of θ)

⇒ sinθ ≈ θ  = 0.003

∴ The angular separation b/w 1st & 2nd minima is 0.003.

Answer 2

Given information,

A parallel beam of light of wavelength 6000 A.U. is incident normally on a narrow slit of width 0.2 mm. The angular separation between first and second minima is:

• (a) 0.003 rad
• (b) 0.006 rad
• (c) 0.5 degree
• (d) 0.3 degree

◐ λ = 6000 A.U.

ㅤ = 6000 × 10^-10

ㅤ = 6 × 10^-7 m.

◐ d = 0.2 mm

ㅤ = 0.2 × 10^-3

ㅤ = 2 × 10^-4 m.

We know that,

✪ λ = d × sinθ ✪

Putting all values,

➻ 6 × 10^-7 = 2 × 10^-4 × sinθ

➻ sinθ = (6 × 10^-7)/(2 × 10^-4)

➻ sinθ = (3 × 10^-7)/(10^-4)

➻ sinθ = 3 × 10^(-7 + 4)

➻ sinθ = 3 × 10^-3

➻ sinθ = 0.003

• Henceforth, the angular separation between first and second minima is 0.003 rad. So, option (a) 0.003 rad is correct!

Explore More,

• Wavelength

The distance between two crests or toughs of wave. Wavelength is measured in the direction of wave. (Longer the wavelength, lower the frequency).

• Angular separation

Angular separation is the angle between two sightlines or two point objects viewed from observer.

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