Question

Light of wavelength $\mathit{\lambda }$and frequency v passes through a single slit of width a. The diffraction pattern is observed on a screen a distance x from the slit. Which of the following will decrease the width of the central maximum? (a) Decrease the slit width; (b) decrease the frequency v of the light; (c) decrease the wavelength $\mathit{\lambda }$of the light; (d) decrease the distance of the screen from the slit. In each case justify your answer.

Short answer

The correct option is (c) to decrease the wavelength of light.

Step-by-step solution

define single slit diffraction

When monochromatic light is sent through a narrow slit, produces a diffraction pattern on a distant screen which is single slit diffraction. The diffraction pattern contains dark and bright regions creating a fringe-like pattern. Dark fringe where destructive interference occurs and bright fringe where constructive interference occurs. In midst of dark and bright fringes, there is the brightest spot which is called the central maxima. The intensity of bright fringes keeps on decreasing as the fringe gets away from the central maxima.

Write the formula of the width of central maxima

Light of wavelength $\left(\lambda \right)$and frequency $\left(v\right)$passes through a single slit of width ( a ) .The diffraction pattern is observed on a screen a distance from the slit. The width of central maxima is given as-

$w=\frac{2\lambda }{a}$

As clear from above expression that

(a) Decreasing the slit width (a) will increase the width of central maxima, as they are inversely proportional to each other.

(b) Decreasing the frequency increases the wavelength of light. As the wavelength is directly proportional to the width of central maxima. Thus, width of central maxima will increase.

(c) Decreasing the wavelength decreases the width of central maxima, as they are directly proportional to each other.

(d) Distance of slit from screen doesn’t affect the width of central maxima so decreasing the distance will have no influence on width of central maxima.

Therefore, only decreasing the wavelength leads to decrease of central maxima.