A laser beam passes through a grating and produces a first-order maximum at an angle of 25°. At what angle is the second-order maximum?
A) 75°
B) 58°
C) 50°
D) 35°
E) 27°

Question

Quizplus · Accepted Answer

For a diffraction grating, the angle $	heta$ of the order maximum is given by $d\sin(	heta) = m\lambda$, where $d$ is the spacing between the grating lines, $\lambda$ is the wavelength of light, and $m$ is the order of the maximum.

For the first-order maximum, we have $m=1$ and $	heta=25^\circ$. Let us assume that the wavelength of light is $\lambda$. Then,

$$d\sin(25^\circ) = \lambda$$

For the second-order maximum, we have $m=2$. Let us assume that the angle of this maximum is $	heta'$ and substitute this into the equation above. Then,

$$d\sin(	heta') = 2\lambda$$

Now, we can divide these two equations to eliminate $d$:

$$\frac{\sin(	heta')}{\sin(25^\circ)} = 2$$

Solving for $	heta'$ gives:

$$	heta' = \sin^{-1}(2\sin(25^\circ)) \approx 57.8^\circ$$

Therefore, the angle of the second-order maximum is approximately 58°, which corresponds to choice (B).

A Laser Beam Passes Through a Grating and Produces a First-Order