How Many Bright Spots Are Visible When Laser Shines Through Slits?

[hellowmad]

Homework Statement

The 480 nm laser is incident on an opaque barrier with a single slit of width 8.0 x 10-5 m. A screen to view the light intensity pattern is 2.0 m behind the barrier. Then a 2nd slit of the same width is made in the barrier. The centers of the slits are 2.4 x 10-4 m apart. Approximately how many smaller bright spots are now observable within the central bright region?

Relevant Equations

d sinθ = mλ for m = 0, 1, -1, 2, -2, 3, -3, 4, -4, ….(constructive)
d sinθ = (m + 1/2 λ) for m = 0, 1, -1, 2, -2, 3, -3, 4, -4, ….(destructive)
x =λml/d
.

The angular position of t)he first diffraction minimum is θ≈sinθ= λ/a, and dsinθ=mλ, so m = (dsinθ) /=[d(λ/a)]/λ =d/a = (2.4 x 10-4 m)/(8.0 x 10-5 m) =3.
Since both bright and dark pots separated on both sides of central bright region, so the smaller bright spots observable within the central bright region is -2, -1, 0, 1, and 2, which leads to total 5.
I want to see if I do it right.
Thanks

 

[BvU]

I want to see if I do it right.

Well, there's a picture here. Is that what you mean with your question ?

(PF doesn't really do approval stamps .)

$\$

 

[haruspex]

Homework Statement: The 480 nm laser is incident on an opaque barrier with a single slit of width 8.0 x 10-5 m. A screen to view the light intensity pattern is 2.0 m behind the barrier. Then a 2nd slit of the same width is made in the barrier. The centers of the slits are 2.4 x 10-4 m apart. Approximately how many smaller bright spots are now observable within the central bright region?
Relevant Equations: d sinθ = mλ for m = 0, 1, -1, 2, -2, 3, -3, 4, -4, ….(constructive)
d sinθ = (m + 1/2 λ) for m = 0, 1, -1, 2, -2, 3, -3, 4, -4, ….(destructive)
x =λml/d
.

The angular position of t)he first diffraction minimum is θ≈sinθ= λ/a, and dsinθ=mλ, so m = (dsinθ) /=[d(λ/a)]/λ =d/a = (2.4 x 10-4 m)/(8.0 x 10-5 m) =3.
Since both bright and dark pots separated on both sides of central bright region, so the smaller bright spots observable within the central bright region is -2, -1, 0, 1, and 2, which leads to total 5.
I want to see if I do it right.
Thanks

Looks right to me.

 

[hellowmad]

Well, there's a picture here. Is that what you mean with your question ?

(PF doesn't really do approval stamps .)

$\$

Yes it is want I mean. Thanks.

 

[hellowmad]

Looks right to me.

thank for checking