Question

What must be the ratio of the slit width to the wavelength for a single to have the first diffraction minimum at 45.00 ?​

Answer 1

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Answer 2

Given:

The first diffraction minimum at 45.00

To find:

What must be the ratio of the slit width to the wavelength for a single to have the first diffraction minimum at 45° ?​

Solution:

From given, we have,

The first diffraction minimum at 45°

Here we will use the direct formula to find the ratio of the slit width to the wavelength for a single.

The formula is given as follows.

a sin ∅ = m λ

For m = 1 (we obtain the first minima value)

substitute the values in the above equation.

a sin 45° = (1) λ

Now find the ratio of the slit width to the wavelength.

By rearranging the terms, we get,

a/λ = 1/sin 45°

we know the value of sin 45°, sin 45° = 1/√2

now substitute the value of the angle in the above equation.

So, we get,

a/λ = 1/(1/√2)

a/λ = √2

Therefore, the ratio of the slit width to the wavelength for a single to have the first diffraction minimum at 45° is √2.