Light diffraction

[NA19]

Question:
If a beam of red light (wavelength = 0.65 micrometres) passes through a pinhole with diameter of 4 micrometres, what is the diameter of the spot on a wall 3 m beyond the pinhole?

Ans: 0.5 m

See attached explanation.

My question is, why can you multiply D by the angle to get lspot?

---

Members don't see this ad.

 

[sps27]

Question:
If a beam of red light (wavelength = 0.65 micrometres) passes through a pinhole with diameter of 4 micrometres, what is the diameter of the spot on a wall 3 m beyond the pinhole?

Ans: 0.5 m

See attached explanation.

My question is, why can you multiply D by the angle to get lspot?

So obviously this is about Diffraction and there is a simple formula to solve questions like this and it is

diameter of the bright spot in the center = wavelength * distance between pinhole and screen / diameter of pinhole.

So I just use that eqn to get to the ans i.e., 3*0.65/4. No need to get into angle theta business, I think.

 

[ashtonjam]

This might help: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinslit.html#c1

The angle theta is actually an approximation. In reality, the equation is tan(&#952=y/D. At low values of θ, tanθ = sinθ = θ. Though I'm not actually sure how that leads to diameter since y is just distance away from the center line.

diameter of the bright spot in the center = wavelength * distance between pinhole and screen / diameter of pinhole. So I just use that eqn to get to the ans i.e., 3*0.65/4

This is right, but just to clarify for others, the units are meters * micrometers / micrometers so you're allowed to just plug in 0.65 and 4 rather than 0.65e-6 and 4e-6 since micrometers cancel.The equation appears in the hyperphysics link above as y = mλD/a.

 

[drechie]

EDIT: What does the "M" mean in the equation that was linked above:

y = m * lamda * D / a

it stands for "order?"