Light from a lamp,which emits light at several discreet different wavelengths,illuminates an 800 line/mm diffraction grating.A screen is placed 50.0 cm behind the grating where the light is observed.Light of wavelength 501.5 nm creates a first-order bright fringe 21.90 cm from the central maximum.What is the wavelength of the bright fringe that is 34.20 cm from the central maximum?
A)706 nm
B)783 nm
C)852 nm
D)920 nm

Question

Quizplus · Accepted Answer

The position of the bright fringe is given by the formula $ y = \frac{m \lambda L}{d} $, where $ m $ is the order, $ \lambda $ is the wavelength, $ L $ is the distance to the screen, and $ d $ is the grating spacing. For the first-order fringe, $ m = 1 $. Given $ y_1 = 21.90 $ cm for $ \lambda_1 = 501.5 $ nm, and $ y_2 = 34.20 $ cm, we can solve for $ \lambda_2 $ using the ratio $ \frac{y_2}{y_1} = \frac{\lambda_2}{\lambda_1} $. Solving gives $ \lambda_2 = 706 $ nm.

Light from a Lamp,which Emits Light at Several Discreet Different