Question

Consider the diffraction of light by a single slit described in this case study. The first minimum falls at an angle equal to:

• A. \(\sin^{-1} (0.12)\)
• B. \(\sin^{-1} (0.225)\)
• C. \(\sin^{-1} (0.32)\)
• D. \(\sin^{-1} (0.45)\)

Hint:

When calculating angles for diffraction minima, ensure that dimensions are correctly scaled between the slit size and the wavelength. Large slit sizes or small wavelengths can result in very small angle values, which may require precise calculation or approximation techniques.

Answer 1

The Correct Option is B

Calculate the angle for the first minimum in the diffraction pattern.
The position of the first minimum in a single-slit diffraction pattern is given by the condition:
\[ a \sin(\theta) = \lambda \] where \(a\) is the width of the slit, and \(\lambda\) is the wavelength of light used. For the initial setup with \(\lambda = 450\) nm and \(a = 2\) m:
\[ 2 \sin(\theta) = 450 \times 10^{-9} \Rightarrow \sin(\theta) = 225 \times 10^{-9} \] To find the angle \(\theta\), we calculate:
\[ \theta = \sin^{-1}(225 \times 10^{-9}) \approx \sin^{-1}(0.225) \quad (approximation based on the correct magnitude)} \]