A single slit forms a diffraction pattern,with the first minimum at an angle of 40.0° from central maximum,when monochromatic light of 630-nm wavelength is used.The same slit,illuminated by a new monochromatic light source,produces a diffraction pattern with the second minimum at a 60.0° angle from the central maximum.What is the wavelength of this new light?
A) 425 nm
B) 450 nm
C) 475 nm
D) 500 nm
E) 525 nm

Question

Quizplus · Accepted Answer

The correct answer is A.The diffraction pattern is given by the equation:d*sin(theta) = m*lambdawhere d is the slit width, theta is the angle from the central maximum, m is the order of the minimum, and lambda is the wavelength of light.For the first minimum, m = 1 and theta = 40.0°. So, we have:d*sin(40.0°) = 1*630 nmd = 630 nm / sin(40.0°) = 798.6 nmFor the second minimum, m = 2 and theta = 60.0°. So, we have:d*sin(60.0°) = 2*lambdalambda = d*sin(60.0°) / 2 = 798.6 nm * sin(60.0°) / 2 = 425 nmTherefore, the wavelength of the new light is 425 nm.

A Single Slit Forms a Diffraction Pattern,with the First Minimum