Two narrow slits, their centers separated by 15 cm, are illuminated by monochromatic radiation and produce the pattern in the figure on a distant screen. The wavelength of the radiation is
A) 0.52 cm
B) 1.0 cm
C) 1.6 cm
D) 2.1 cm
E) 3.0 cm

Question

Two narrow slits, their centers separated by 15 cm, are illuminated by monochromatic radiation and produce the pattern in the figure on a distant screen. The wavelength of the radiation is
A) 0.52 cm 
B) 1.0 cm 
C) 1.6 cm 
D) 2.1 cm 
E) 3.0 cm

Quizplus · Accepted Answer

The distance between the central bright fringe and the first bright fringe on either side is given by:
d sin θ = λ , where d is the slit separation, θ is the angle between the line connecting the slit centers and the line from the slits to the fringe,
and λ is the wavelength of light.
We can observe from the figure that the distance between the central bright fringe and the first bright fringe on either side is approximately the same as the distance between the two central maxima. 
Therefore, we can estimate the wavelength of the light to be approximately twice the distance between the central maxima.
Using the figure, we can estimate the distance between the central maxima to be around 2 cm. Therefore, the wavelength of the light is approximately 2 x 1 cm = 2 cm.
The closest answer choice is B) 1.0 cm.

Two Narrow Slits, Their Centers Separated by 15 Cm, Are