Suppose you have measured the diffraction pattern of a grating with d = 0.19 mm and have found that the spots were separated by s = 1.8 cm. Now you want to determine d for an unknown grating. With the unknown grating, the spots are separated by s = 4.5 cm. What is d (mm) ?

d = 0.076 mm

Explanation:

Given data

diffraction pattern d1 = 0.19 mm = 0.019 cm

separated s (1) = 1.8 cm

separated s (2) = 4.5 cm

to find out

d2 for an unknown

solution

we know here that spacing in between the diffraction fringe is always inversely proportional to diffraction grating so

we will apply here formula for unknown d that is

d1 (s1 / L) = d2 (s2 / L)

d2 = d1 * s (1) / s (2)

put here all thes evalue we get d2

d2 = d1 * s (1) / s (2)

d2 = 0.019 * 1.8 / 4.5

d2 = 0.0076 cm

d2 = 0.076 mm