Answer to Question #122089 in Optics for Mio

Question #122089
Diffraction grating A has 16 000 lines/cm, and diffraction grating B has 12 000 lines/cm. Light of the same wavelength is sent through both gratings to a screen located a distance L from the gratings. The spacing of the maxima for grating A is 3.46 cm. What is the spacing for the maximum for grating B?
1
Expert's answer
2020-06-17T09:34:47-0400

Given:

dA=1/16000 cm1dB=1/12000 cm1xA=3.46 cm.d_A=1/16 000 \text{ cm}^{-1}\\ d_B=1/12 000 \text{ cm}^{-1}\\ x_A=3.46\text{ cm}.

Solution

The fringe spacing can be expressed as


x=λLd,x=\frac{\lambda L}{d},

where L - distance from the screen.

Thus, for A we have


xA=λLdA,λL=xAdA.x_A=\frac{\lambda L}{d_A},\\ \lambda L=x_Ad_A.

For B:


xB=λLdB=λLdB=xAdAdB=3.461200016000=2.60 cm.x_B=\frac{\lambda L}{d_B}=\frac{\lambda L}{d_B}=x_A\frac{d_A}{d_B}=3.46\cdot\frac{12000}{16000}=2.60\text{ cm}.

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