Number of lines/cm for the grating

[physicsstoodent]

The problem is:

Three, and only three, bright fringes can be seen on either side of the central maximum when a grating is illuminated with light ( = 520 nm). What is the maximum number of lines/cm for the grating?

Here is what i know / did:

since there are three fringes, m = 3

since they are bright fringes, it's constructive interference so (m lambda)

we know that d sin(theta) = (m lambda)

so, d sin(theta) = (3 * 5.20 E-7 meters)

we know that the highest displacement has to occur when theta is 90 degrees. So, sin of 90 gives you 1.

d sin(90) = (3 * 5.2 E -7); D = 1.56 E-6 meters <- This is the slit separation, I am stuck at this point.

 

[physicsstoodent]

Never Mind

I figured it out

Nmax = 1 / D min

since d = 1.54 E-6 m = 1.5 E -4 cm

1 / 1.54 E -4 cm = 6410 lines/cm.

 

[m2003]

Based on the given information, we can calculate the maximum number of lines per centimeter for the grating.

First, we need to find the slit separation (d) using the equation d sin(theta) = m lambda, where d is the slit separation, theta is the angle of diffraction, m is the number of fringes, and lambda is the wavelength of light.

We know that theta is 90 degrees for the maximum displacement, sin(90) = 1. Therefore, we can rearrange the equation to solve for d:

d = (m lambda) / sin(theta)

Substituting the given values, we get:

d = (3 * 520 nm) / 1

d = 1560 nm = 1.56 micrometers

Now, to find the number of lines per centimeter, we need to convert this value to centimeters and divide it by the width of the grating (w).

Number of lines/cm = (1 cm / 1.56 micrometers) / w

Since we do not have information about the width of the grating, we cannot determine the exact number of lines per centimeter. However, we can say that the maximum number of lines per centimeter for the grating is approximately 640,000 (assuming a standard grating width of 1 cm).

In conclusion, the maximum number of lines per centimeter for the grating is approximately 640,000.