How to find LASER (Light Amplification by Stimulated Emission of Radiation) wavelength using a Diffraction Grating in the Lab. For this just take a LASER source, a grating (here grating have 15000 lines per inch), and a screen to observe the diffraction pattern.

When a LASER light passes through the Grating its diffracted and a pattern develops on the screen with central maxima. Diffraction is a phenomenon of light, in which wave light bends at the edges of an obstacle, if and only if the size of the obstacle is comparable to the wavelength of the light. These diffracted waves superimpose further and a constructive interference appears on the screen. If your aim is to find the wavelength by this experiment then, first find the single slit width; that is known as the grating element and denoted by “d”. This you can find out from the lines that are mentioned on the grating as here 15000 LPI. One inch is 2.54 cm so 15,000 lines are in 2.54 cm so one line will be equal to 2.54/15000 cm. This is 1.69×10^ (-4)cm approximately.

We have to use nk=2d sin theta

where k is the wavelength; that is to be found from observation

n= is the order of diffraction

d= is the grating element

and theta is the angle between the line (distance between the screen and grating) and first maxima on either side if an observation is for the first order.

we have already found out the “d” grating element, n=1 for first order now we have to find the “theta” that can be find out using the “Tan theta” i.e. basically ratio of the distance from central maxima to the first order maxima (you can say Y) and the distance between screen and grating that is D. Now “tan theta = Y/D” from this you can find the theta which can be used to calculate the value of “sin theta”. Now you can put these value and find the result for wavelength (lambda). You can take different observations for the “theta”….by varying the distance “D” and “Y”. Take the average and find the wavelength.

Now compare this result with the standard value of the laser light and check the percentage error. Your % error is the result of varying designing parameters of the LASER (Light Amplification by the Stimulated Emission of Radiation) and manual error.

And more about the type of emission (Stimulated Emission ) you can see

https://www.youtube.com/watch?v=Rpq7A_Efp2k&list=TLidLhgGyonm4XQOYdai0Nl4FAgJgrfpQW