A Level Physics Practice Exam

What is the angle of diffraction for the second order diffracted beam when monochromatic light of wavelength 590 nm passes through a grating with spacing of 1.67 × 10^-6 m?

1. 30.0 degrees

2. 45.0 degrees

3. 50.0 degrees

4. 60.0 degrees

The correct answer is: 45.0 degrees

To determine the angle of diffraction for the second order diffracted beam, we can use the grating equation, which is given by: \[ d \sin(\theta) = m \lambda \] where \( d \) is the grating spacing, \( m \) is the order of diffraction, \( \lambda \) is the wavelength of the light, and \( \theta \) is the angle of diffraction. In this case: - The wavelength \( \lambda = 590 \, \text{nm} = 590 \times 10^{-9} \, \text{m} \), - The grating spacing \( d = 1.67 \times 10^{-6} \, \text{m} \), - The order \( m = 2 \) for the second order beam. Substituting these values into the grating equation: \[ 1.67 \times 10^{-6} \sin(\theta) = 2 \times (590 \times 10^{-9}) \] Calculating the right-hand side: \[ 2 \times (590 \times 10^{-9}) = 1180 \times 10^{-9} = 1.18