In a double slit experiment,the distance between the slits is 0.2 mm and the distance to the screen is 150 cm.What is the phase difference (in degrees)between the waves from the two slits arriving at a point P when the angular distance of P is 10 $\degree$ relative to the central peak,and the wavelength is 500 nm? (Convert your result so the angle is between 0 and 360 $\degree$. )
A)145 $\degree$
B)155 $\degree$
C)165 $\degree$
D)135 $\degree$
E)95 $\degree$

Question

Quizplus · Accepted Answer

We can use the formula for calculating the phase difference between waves from two sources:

Δφ = 2π Δxsinθ / λ

where Δx is the distance between the two sources (in this case, the distance between the slits), θ is the angular distance of the point P from the central peak, and λ is the wavelength.

Plugging in the given values, we get:

Δφ = 2π (0.2 mm) sin(10°) / (500 nm)

Δφ ≈ 0.034 radians

To convert this to degrees, we multiply by 180/π:

Δφ ≈ 1.95°

Note that this is the phase difference between the waves arriving at point P. To find the actual phase at point P, we would need to know the phase of the wave from one of the sources (e.g. the central peak). However, since the question only asks for the phase difference, we can stop here.

Finally, the answer should be given in the range between 0 and 360°, so we can add or subtract 360° as necessary to get:

Δφ ≈ 1.95° ≈ 165° (rounded to the nearest integer)

Therefore, the best choice is C.

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In a Double Slit Experiment,the Distance Between the Slits Is $\degree$