Question

Muscle contractions change striation distances from 1.87 to 1.94 micrometers. These changes are measured by shining a beam of laser light with a wavelength of 650 nm onto a tank of freshwater containing glass catfish. The diffraction pattern is directed onto a screen that is 30cm behind the fish. Investigators measured the change in the location of the m=1 diffraction spot as the fish swam in front of the beam. What is the distance that the diffraction spot moved on the screen?

Answer 1

The distance that the diffraction spot moved on the screen is 0.314 cm

Step-by-step explanation:

The condition for maxima is equal:

`sin\theta _(max) =(\lambda )/(D*1.33)\\\theta _(max) =sin^(-1) (\lambda )/(D*1.33)`

Where

λ = 650 nm = 650x10⁻⁹m

D = distances = 1.87 μm = 1.87x10⁻⁶m and 1.94x10⁻⁶m

Replacing:

`\theta _(1.87) =sin^(-1) (650x10^(-9) )/(1.87x10^(-6)*1.33 ) =15.15`

`\theta _(1.94) =sin^(-1) (650x10^(-9) )/(1.94x10^(-6)*1.33 ) =14.59`

The distance that the diffraction spot moved on the screen is equal to:

`x=d*(tan\theta _(1.87) -tan\theta _(1.94) )=30*(tan15.15-tan14.59)=0.314cm`