What will be the angle of diffraction for the first secondary maximum due to diffraction at a single slit of width 0.5 mm and using light off 5000 Å?

• A: 1.5 × 10⁻⁴ radian
• B: 1.5 × 10⁻³ radian
• C: 0.75 × 10⁻³ radian
• D: 0.001 radian

To find the angle of diffraction for the first secondary maximum in a single slit diffraction pattern, we can use the formula:

Key Formula

The angle θ for the first secondary maximum can be approximated using:

a sin(θ) = mλ

where:

• a = width of the slit
• m = order of the maximum (for the first secondary maximum, m = 1)
• λ = wavelength of light

Given Values

• Width of the slit, a = 0.5 mm = 0.5 × 10⁻³ m
• Wavelength of light, λ = 5000 Å = 5000 × 10⁻¹⁰ m = 5 × 10⁻⁷ m

Calculation Steps

Substituting the values into the formula:

0.5 × 10⁻³ sin(θ) = 1 × 5 × 10⁻⁷

Solving for sin(θ):

sin(θ) = (5 × 10⁻⁷) / (0.5 × 10⁻³) = 1 × 10⁻³

Finding the Angle

Now, we can find θ:

θ ≈ sin⁻¹(1 × 10⁻³)

For small angles, sin(θ) ≈ θ in radians, so:

θ ≈ 1 × 10⁻³ radian

Final Answer

The angle of diffraction for the first secondary maximum is approximately 0.001 radian, which corresponds to option D.