A Level Physics Practice Exam

What happens to the angle θ for the first order beam if the wavelength of the monochromatic light decreases?

1. Angle θ gets larger

2. Angle θ gets smaller

3. Angle θ remains unchanged

4. Angle θ fluctuates

The correct answer is: Angle θ gets smaller

When the wavelength of the monochromatic light decreases, the angle θ for the first-order beam in a double-slit or diffraction grating experiment also decreases. This relationship can be understood through the underlying physics of interference patterns. The angle θ is determined by the equation for constructive interference, which can be expressed as: \[ d \sin(\theta) = n \lambda \] where \( d \) is the distance between the slits, \( n \) is the order of the interference (in this case, first order means \( n = 1 \)), and \( \lambda \) is the wavelength of the light. As the wavelength \( \lambda \) decreases, to maintain the equality in the equation, the sine of the angle \( \theta \) must also decrease, assuming the distance \( d \) remains constant. Since the sine function is a monotonically increasing function, a smaller wavelength leads to a smaller angle for the first-order maximum. This means as the wavelength gets shorter, the angle at which we observe the first-order maximum becomes smaller, resulting in a tighter interference pattern.