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max2010maxim [7]
3 years ago
5

580 nm light shines on a double slit

Physics
1 answer:
lesantik [10]3 years ago
6 0

Answer:

Angular position of the first minimum is 0.27 degree

Explanation:

As we know by the formula of single slit diffraction pattern

a sin\theta = m\lambda

here we have

a = d = 0.000125 m

for m = 1

\lambda = 580 nm

now we have

0.000125 sin\theta = 580 \times 10^{-9}

sin\theta = 4.64 \times 10^{-3}

\theta = 0.27 degree

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<h2>Answer:</h2>

(a) standard deviation = σ = 4.9996

(b) variance = σ² = 24.996

<h2>Explanation:</h2><h2 />

<em>Given frequency table (find attached as Table 1);</em>

<u></u>

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=> c = (6.51 + 8.50) / 2 = 7.505

=> c = (8.51 + 10.50) / 2 = 9.505

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=> c = (12.51 + 14.50) / 2 = 13.505

=> c = (14.51 + 16.50) / 2 = 15.505

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The variance is calculated using the following formula

σ² = [Σ(f x c²) - (n x M²)] / (n - 1)                ------------(i)

Where;

f = frequency of each boundary data point

<em>=>  Let's first calculate </em>Σ(f x c²).

This is done by finding the sum of the product of the frequency (f) of each boundary point and the square of their corresponding mid-points(c)

Σ(f x c²) = [(50 x 7.505²) + (18 x 9.505²) + (42 x 11.505²) + (20 x 13.505²) + (46 x 15.505²)]

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σ² = [Σ(f x c²) - (n x M²)] / (n - 1)

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σ² = [4374.3708] / (175)

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Therefore, the variance is 24.996

<em>v. Find the standard deviation (σ)</em>

The standard deviation is the square root of the variance. i.e

σ = √σ²

σ = √24.996

σ = 4.9996

Therefore, the standard deviation is 4.9996

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