Question

1. What would happen to the single slit pattern on the wall if the wavelength of the laser were increased? Explain your reasoning.

a) How would the pattern change if the single slit were made narrower? Why?

b)How would the pattern change if a grating with a larger slit density were used? Why?

c) If you look at a compact disk under a bright light you can see a spectrum at some angles. Explain why this happens.

d)What would your pattern look like if your light source had a mixture of discrete colors like the spectrum tubes you used in the prism experiment?

Answer 1

1] The spacing between the fringes obtained with single slit [whose width is of the order of the wavelength] is:

so, if the wavelength of the light source is increased, the separation between the fringes x, increases and thus the fringes will be more spread out on the screen.

a] Alternatively, if the slit width d is made smaller, while the wavelength remains the same, the fringe separation will again increase (since the denominator decreases) and the fringes will be more spread out on the screen.

b] A larger slit density implies that there will be more slits packed in the same length of the slit. This means that the slit separation will be lesser.

Spacing between the fringes in this case will be:

where a is the slit separation. So, if a larger slit density is used, a decreases thereby increasing x which means that the fringes will be more spread out on the screen.

c] The colors emerge from the back of a CD because it consists of concentric ridges which are evenly distributed and whose separation is of the order of the wavelength of light in visible region and so it acts like a reflective grating for dispersing light.

d] There would be an interference pattern for each wavelength in the source and these patterns will be separated by an offset on the screen since a larger wavelength will have larger fringe separation. So, if one were to analyze a first order maxima, blue light will have its maxima closest to the central bright spot (which will be white) since it has the smallest wavelength and red will have its maxima farthest from the central bright spot because it has the largest wavelength.