# What is the angular width of the central maximum?

A single slit of width 1.50 um is illuminated with light of wavelenth 500.0 nm. What is the angualar width of the central maximum?

Related Introductory Physics Homework Help News on Phys.org
Hootenanny
Staff Emeritus
Gold Member
Please show some work or initial thoughts.

~H

the answer in the book is 38.9 degrees but how is this right?

I tried the formula &= wavelenth / b and came up with (5 * 10^-9) / (1.5 *10^-6) and got 3.33 * 10^-3 then multiplied this by 2. is this right?

anymore ideas anyone ???

Hootenanny
Staff Emeritus
Gold Member
The answer in the book is correct. You are simply a factor of $10^{2}$ out with respect to the $\sin\theta$. Your error lies here:

wayneo said:
(5 * 10^-9) / (1.5 *10^-6)
$$500nm \neq 5\times 10^{-9}m$$

Recheck your calculation. Also you need to find the angle (ArcSin)

~H

Last edited:
nrqed
Homework Helper
Gold Member
wayneo said:
I tried the formula &= wavelenth / b and came up with (5 * 10^-9) / (1.5 *10^-6) and got 3.33 * 10^-3 then multiplied this by 2. is this right?
first, 500 nm = 500 times 10^-9.

The second thing is that what you found is sin(theta). To find the *angle* you must do the inverse sin of that. Then multiply the result (in degrees) by two

thanks guys it works, just made a silly error!