Question

How wide is the central diffraction peak on a screen 2.40 m behind a 0.0368-mm-wide slit illuminated by 578-nm light? Express your answer using three significant figures.

Answer 1

The width of the central diffraction peak on the screen can be calculated using the formula (λ * D) / (w). After plugging in the given values, the width is calculated to be 376.9 mm.

Step-by-step explanation:

The width of the central diffraction peak on a screen behind a slit can be determined using the formula:

Width = (λ * D) / (w)

Where λ is the wavelength of the light, D is the distance between the screen and the slit, and w is the width of the slit. Plugging in the given values, we get:

Width = (578 nm * 2.40 m) / (0.0368 mm)

Converting the units and performing the calculation, we find that the width of the central diffraction peak is 376.9 mm.

Answer 2

The width of the central diffraction peak is 0.0754 m.

Step-by-step explanation:

Given:

Distance of screen from slit (L) = 2.40 m

Width of the slit (a) = 0.0368 mm = 0.0368 × 10⁻³ m

Wavelength of light (λ) = 578 nm = 578 × 10⁻⁹ m

Now, we know that, the location of the first diffraction minimum from the center is given as:

`y=(L\lambda)/(a)\\\\Where,y\to\ location\ of\ first\ minimum\ \textrm{diffraction}`

Now, in order to find the width of the central diffraction peak we need to consider the distance 'y' both above and below the central line.

Therefore, the width of the central diffraction peak is given as twice the distance 'y'.

So, Width of central diffraction peak is,
`W=2y=(2L\lambda)/(a)`

Now, plug in the values given and solve for width 'W'. This gives,

`W=(2* 2.40\ m* 578* 10^(-9)\ m)/(0.0368* 10^(-3)\ m)\\\\W=0.0754\ m`

Therefore, the width of the central diffraction peak is 0.0754 m.