Diffraction Grating: Finding Wavelength with Given Angle and Slit Density

AI Thread Summary
To find the wavelength of monochromatic light using a diffraction grating with 5.3x10^3 lines/cm and a first-order maximum at 17 degrees, the correct formula is d(sin Θ) = mλ. The slit separation, d, must be calculated as 1/(5.3x10^3 lines/cm), which equals 1.89x10^-6 m when converted to meters. The angle (Θ) is given as 17 degrees, and using m=1 for the first-order maximum, the equation simplifies to λ = (d sin Θ). The error in the initial calculation arose from not properly accounting for the conversion factor of 10^6 in the slit density, leading to an incorrect wavelength result.
seanmcgowan
Messages
35
Reaction score
0

Homework Statement


Monochromatic light shines on the surface of a diffraction grating with 5.3x10^3 lines/cm. The first order maximum is observed at an angle of 17 (degrees). Find the wavelength.

a) 420nm c) 530nm
b) 520nm d) 550nm


Homework Equations


d(sin \Theta)=m\lambda

d= 5.3x10^lines/cm=5.3x10^3 lines/m

\Theta=17

m (the order maximum)= 1

The Attempt at a Solution


I rearranged the problem so it looked like this: \lambda=(d\Theta)/m

Since m=1, I dropped it and only worked with the numerator.

The distance between the slits is 1/53 metres so the full equation looks like this: (1/53)(sin17)= \lambda

(1/53)(.29)=\lambda
.0054716981=\lambda

Just by looking at this answer its easy to see its wrong, but why? I followed the equation, so what's up? Any help would be appreciated.
 
Physics news on Phys.org
d is not 1/5.3 it is 1/5.3 times 10 to the power of 6.
 
So my work was correct but i just needed that 10^6? thanks for the help
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Diffraction pattern from a grating
Replies
3
Views
844
Balmer series experiment
Replies
2
Views
954
Calculating the Number of Lines for a Diffraction Grating
Replies
3
Views
2K
Number of bright fringes given by diffraction grating on a screen
Replies
6
Views
3K
Diffraction Grating: Possible variables for Experiment
Replies
5
Views
2K
Diffraction Grating wavelength
Replies
3
Views
2K
Diffraction Grating Vs Double-Slit: Small angle Approx.
Replies
1
Views
8K
Electron Velocity Diffraction Grating Problem
Replies
4
Views
1K
Maxima in a diffraction grating
Replies
2
Views
3K
Diffraction grating problem involving Snell's Law
Replies
3
Views
5K

Hot Threads

Recent Insights

Back
Top