Question

Does the spacing between fringes in a two-slit interference pattern increase, decrease, or stay the same if

(a) the slit separation is increased,

(b) the color of the light is switched from red to blue, and

(c) the whole apparatus is submerged in cooking sherry?

(d) If the slits are illuminated with white light, then at any side maximum, does the blue component or the red component peak closer to the central maximum?

Short answer

(a) Increase in slit separation decreases the spacing between fringes.

(b) Switch of the color of light from red to blue decreases the spacing between fringes.

(c) If the whole apparatus is submerged in cooking sherry the spacing between fringes decreases.

(d) The peak from the blue component is closer to the central maximum than the peak from the red component.

Step-by-step solution

Given data:

Interference from a pair of slits.

Interference fringe width:

The interference fringefor slit separation $\mathit{d}$, screen distance$\mathit{D}$ ,and wavelength$\mathit{\lambda }$ is

$\mathbf{∆}\mathit{x}\mathbf{=}\frac{\mathbf{\lambda }\mathbf{D}}{\mathbf{d}}$….. (1)

(a)Determining the change in fringe width with an increase in slit separation:

From equation (1) the fringe width is inversely proportional to the separation of the two slits. Thus, if slit separation is increased the fringe width will decrease.

(b) Determining the change in fringe width with the change in wavelength:

From equation (1) the fringe width is directly proportional to the wavelength of incident light. The wavelength of red light is greater than the wavelength of blue light. When light is switched from red to blue the wavelength decrease, thus the fringe width also decreases.

(c) Determining the change in fringe width with the change in the refractive index:

From equation (1) the fringe width is directly proportional to the wavelength of incident light. Cooking sherry has a refractive index greater than air. Thus,the wavelength of light in cooking sherry will be lower than that in air. Thus, the fringe width decreases.

(d) Determining the fringe width for blue and red:

It has previously been shown that the fringe width for blue light is smaller than the fringe width for a red light. Thus, when the incident light is white containing all the colors, the non-zero order maxima from blue light will be closer to the central maxima than the non-zero order maxima from red.