Calculating Wavelength of Laser Beam using Single Slit

[map7s]

A laser beam passes through a single slit of width 0.0186 mm and produces a pattern with an intensity distribution like that shown in Figure 13a (page 208), on a screen 105.6 cm away. If the spacing between the minima on either side of the central maximum is 7.16 cm (in other words, 2y1 in Figure 13b, page 208), the wavelength of the light is ? nm.

I have absolutely no idea how to start this problem. I know that i read something in my textbook about how with intensity of laser beams need to be calculated thru E

wavelength=c/f

E=hf

E=hc/wavelength

h=6.63E-34

but I did not know if I had to/how to use these equations in this problem.

 

[Hootenanny]

Perhaps this will be helpful;

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinslit.html

 

[m2003]

I would first identify the relevant equations and principles that apply to this problem. In this case, the equation for calculating the wavelength of light is relevant, as well as the principles of diffraction and interference.

Next, I would carefully read the information given in the problem and identify the known values and the unknown value that needs to be calculated. In this case, the known values are the width of the slit (0.0186 mm), the distance to the screen (105.6 cm), and the spacing between the minima (7.16 cm). The unknown value is the wavelength of the light.

To solve for the wavelength, I would use the equation for the spacing between the minima, which is given as 2y1 in Figure 13b. This equation is:

2y1 = (λD)/w

where λ is the wavelength, D is the distance to the screen, and w is the width of the slit.

Substituting the known values into this equation, we get:

7.16 cm = (λ * 105.6 cm)/0.0186 mm

Solving for λ, we get:

λ = (7.16 cm * 0.0186 mm)/105.6 cm = 0.0012636 mm = 1.2636 μm

Therefore, the wavelength of the light is 1.2636 micrometers or 1263.6 nanometers.

In conclusion, the calculation of the wavelength of a laser beam passing through a single slit involves using the principles of diffraction and interference and the relevant equations to solve for the unknown value.