A Level Physics Practice Exam

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

1. The angle θ increases

2. The angle θ remains unchanged

3. The angle θ decreases

4. The angle θ fluctuates

The correct answer is: The angle θ decreases

In the context of diffraction or interference patterns, the angle θ for the first-order beam is related to the wavelength of the light used. Specifically, for a single-slit or double-slit experiment, the condition for destructive or constructive interference is given by a formula that involves both the wavelength and the angle of the order observed. For first-order interference, the angle θ can be described with the formula: \[ d \sin \theta = n \lambda \] where \( d \) is the slit separation, \( n \) is the order number (1 for first-order), and \( \lambda \) is the wavelength of light. As \( \lambda \) decreases while keeping the slit separation \( d \) constant, the product \( n \lambda \) becomes smaller, which means that \( d \sin \theta \) must also decrease in order to maintain equality. Since \( d \) is fixed, this leads to a decrease in the value of \( \sin \theta \), and consequently, the angle θ must decrease as well in order to satisfy the equation. Hence, the relationship between wavelength and angle is such that a decrease in wavelength results in a decrease in the angle for the first order beam.