Question

In a single-slit diffraction pattern on a flat screen, the central bright fringe is 1.6 cm wide when the slit width is 2.8 × 10-5 m. When the slit is replaced by a second slit, the wavelength of the light and the distance to the screen remaining unchanged, the central bright fringe broadens to a width of 2.3 cm. What is the width of the second slit? It may be assumed that is so small that sin is approximately equal to tan .

Answer 1

Answer 2

We can use the equation for the width of the central bright fringe in a single-slit diffraction pattern on a flat screen, which is given by:

w = (λL) / w

where w is the width of the slit, λ is the wavelength of the light, L is the distance from the slit to the screen, and w is the width of the central bright fringe.

We can rearrange this equation to solve for the slit width w:

w = (λL) / w

w^2 = λL

w = sqrt(λL)

We can use this equation to find the width of the first slit:

w1 = sqrt(λL) = sqrt((0.016 m) x (2.8 x 10^-5 m)) = 5.4 x 10^-7 m

Now, we can use the same equation to find the width of the second slit:

w2 = (λL) / w2

We know that the central bright fringe broadens to a width of 2.3 cm, or 0.023 m. We also know that the wavelength of the light and the distance to the screen remain unchanged. Therefore, we can set up the following equation:

0.023 m = (λL) / w2

Solving for w2, we get:

w2 = (λL) / 0.023 m

Plugging in the values for λ and L, we get:

w2 = (6.626 x 10^-34 m^2 kg/s x 3 x 10^8 m/s) / (0.023 m x 1.5 m)

w2 = 7.16 x 10^-7 m

Therefore, the width of the second slit is 7.16 x 10^-7 m.