Monochromatic light falls on a grating with grating element 1.0 mm at an glancing angle 1o. When it is diffracting at an glancing angle 3.0o the maximum of first order occurs the λ is a. 0.5µm b. 34µm c. 14µm d. 0.8µm?

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Answer

Answer:

Given:
- Grating element, d = 1.0 mm
- Glancing angle of incidence, θ1 = 1°
- Glancing angle of diffraction, θ2 = 3°
- Maximum of first order occurs at λ

To find:
The wavelength of the incident monochromatic light

Solution:

Step 1: Calculate the distance between two consecutive slits in the grating using the formula:
d sin θ = mλ
where,
m = order of diffraction
λ = wavelength of light
d = grating element
θ = angle of diffraction

For maximum of first order, m = 1
So, d sin θ = λ
=> d = λ/sin θ
=> 1.0 × 10^-3 m = λ/sin 3°

Step 2: Convert the grating element to meters for convenience
d = 1.0 mm = 1.0 × 10^-3 m

Step 3: Substitute the value of d in the equation obtained in step 1
1.0 × 10^-3 m = λ/sin 3°
=> λ = 1.0 × 10^-3 m × sin 3°
=> λ ≈ 0.052 µm

Step 4: Compare the calculated value of λ with the given options
The calculated value of λ ≈ 0.052 µm, which is closest to option (a) 0.5 µm.

Therefore, the correct answer is option (a) 0.5 µm.

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