- #1

JJK1503

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## Homework Statement

A Helium laser, λ = 588

*nm*, shines on double-slits separated by 1.80

*mm*. An interference pattern is observed on a screen at a distance R from the slits. The point C on the screen is at the center of the principal maximum of the interference pattern. The point P is the point on the principal maximum at which the intensity of light is half that of the intensity at C. What is the value of the angle θ?

## Homework Equations

I (final) = I (initial) * cos^2( (pi * d * sin(θ)) / λ )

small angle approximation sin(θ) = tan(θ) = θ

## The Attempt at a Solution

On questions like these I typically find it easiest to pick some dummy value and solve. In this case i set I (initial) to 10.

The center of the center maxima is where intensity is the greatest. At this point θ = 0.

so,

I (final) = I (initial) * cos^2( (pi * d * sin(θ)) / λ )

= 10 * cos^2( (pi * d * sin(0)) / λ )

= 10 * cos^2 (0)

= 10

If I want the θ where I (final) = I(initial0 / 2. I need to find θ where I (final) = 10 / 2 = 5

so (with small angle approximation),

I (final) = I (initial) * cos^2( (pi * d * sin(θ)) / λ )

5 = 10 * cos^2( (pi * (1.8 * 10^-3) * θ) / (588 * 10^-9 )

0.5 = cos^2( (pi * (1.8 * 10^-3) * θ) / (588 * 10^-9 )

0.5 = cos^2 (9617.1204 * θ)

At this point I plug the above equation into my calculator and have it solve for θ.

According to my calculator θ = 0.03743 deg

This seems like a reasonable result; However, the computer kicks it out as incorrect.

I am NOT looking for someone to give me this answer. However, ANY help with my method is GREATLY appreciated.

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