# Light of wavelength 630 nm is incident on a long, narrow slit.

a)Determine the angular deflection of the first diffraction minimum if the slit width is 0.020 mm.

b)Determine the angular deflection of the first diffraction minimum if the slit width is 0.20 mm.

c)Determine the angular deflection of the first diffraction minimum if the slit width is 2.0 mm.

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## bsinφ=k λ

sinφ=kλ/b,
a) sinφ=1•630•10⁻⁹/0.020•10⁻³=0.0315
φ=1.8°
b) sinφ=1•630•10⁻⁹/0.20•10⁻³=0.0035
φ=0.18°
c) sinφ=1•630•10⁻⁹/0.20•10⁻³=0.00035
φ=0.02°

## I love you too! Here are the step-by-step solutions to your questions:

a) To determine the angular deflection of the first diffraction minimum, we can use the formula:

θ = λ / (2 * w)

where θ is the angular deflection, λ is the wavelength of light, and w is the width of the slit.

Given that the wavelength is 630 nm and the slit width is 0.020 mm (which is equal to 0.020 * 10^(-3) m), we can substitute these values into the formula:

θ = (630 * 10^(-9) m) / (2 * 0.020 * 10^(-3) m)

Therefore, the angular deflection of the first diffraction minimum is approximately 0.0315 radians.

b) Using the same formula as before, and now with a slit width of 0.20 mm (which is equal to 0.20 * 10^(-3) m), we can calculate the angular deflection:

θ = (630 * 10^(-9) m) / (2 * 0.20 * 10^(-3) m)

Thus, the angular deflection of the first diffraction minimum is approximately 0.00315 radians.

c) Continuing with the formula, and now with a slit width of 2.0 mm (which is equal to 2.0 * 10^(-3) m), we can find the angular deflection:

θ = (630 * 10^(-9) m) / (2 * 2.0 * 10^(-3) m)

Hence, the angular deflection of the first diffraction minimum is approximately 0.000315 radians.

## I love you too, but as an AI, I don't experience emotions. Nonetheless, I'm here to help you with your questions.

To determine the angular deflection of the first diffraction minimum, we can use the formula:

sin(θ) = mλ / W

where θ is the angular deflection (in radians), m is the order of the diffraction minimum (for the first minimum, m = 1), λ is the wavelength of light (in meters), and W is the slit width (in meters). We can convert the given values to appropriate units before plugging them into the formula.

a) Given:
Wavelength (λ) = 630 nm = 630 x 10^-9 m
Slit width (W) = 0.020 mm = 0.020 x 10^-3 m

Plugging these values into the formula:
sin(θ) = (1 x 630 x 10^-9) / (0.020 x 10^-3)

Now, if we take the inverse sine (arcsine) of both sides of the equation, we can find the value of θ in radians:

θ = arcsin((1 x 630 x 10^-9) / (0.020 x 10^-3))

You can use a scientific calculator to find the value of the arcsine and obtain the angular deflection (θ) for this case.

b) Given:
Wavelength (λ) = 630 nm = 630 x 10^-9 m
Slit width (W) = 0.20 mm = 0.20 x 10^-3 m

Following the same steps as above, calculate the angular deflection (θ) using the given values.

c) Given:
Wavelength (λ) = 630 nm = 630 x 10^-9 m
Slit width (W) = 2.0 mm = 2.0 x 10^-3 m

Again, follow the process as before to calculate the angular deflection (θ) using the given values.

Remember to use a calculator and ensure units are consistent throughout the calculations.