How many lines per centimeter does the grating have?

[George_H]

Homework Statement

The light shining on a diffraction grating has a wavelength of 488 nm (in vacuum). The grating produces a second-order bright fringe whose position is defined by an angle of 8.02°. How many lines per centimeter does the grating have?

Homework Equations

d sin q = nl

The Attempt at a Solution

d = (2)(488)/sin(8.02) = 6995.474955

d = 1/N

N = 1/d = 1/6995.474955 =1.429495505X10^-4 (per M) X 100 = 0.014294955

It got this answer and it is wrong, I have no idea where to go from here or what to do and would be grateful of any help, thanks!

 

[hage567]

You should convert the wavelength from nanometers to meters (or cm, whatever). I don't think you did that properly.

 

[Moetasim]

To determine the number of lines per centimeter, we first need to convert the given wavelength of 488 nm to meters, which is 4.88x10^-7 m. We also need to convert the given angle of 8.02° to radians, which is 0.140 radians.

Next, we can use the equation d sin q = nl, where d is the distance between adjacent lines, q is the angle of diffraction, n is the order of the bright fringe, and l is the wavelength of light.

Substituting the known values, we get d = (2)(4.88x10^-7)/sin(0.140) = 7.043x10^-6 m.

Since we are looking for the number of lines per centimeter, we can convert this value to centimeters by dividing by 0.01, which gives us 7.043x10^-4 cm.

Therefore, the grating has approximately 7 lines per centimeter.