Exploring Our Universe:
From the Classroom to Outer Space
II. The FUSE Satellite
Activity #4 Solutions

Step 1 - Reflection

Students should choose drawing C. Check that the normal is perpendicular to the mirror surface and q i  =  qr . Angle measures will vary depending on how the lines are drawn and how the sheets are duplicated. Reasonable numbers are 15o  to 20o .
 

Step 2 – Derive the Grating Equation

The path difference is d sin q . When the path difference is equal to an integer multiple of the wavelength, there is constructive interference.  In symbols:
 

d sin q = m l.
Step 3 - Use the Grating Equation
 
d = 1/5500 lines /mm = 1.82 x 10-4 mm =  1.82 x 10-7 m
m = 1
wavelength    l   (m)
sin q = m l/d
q 
9.1 x 10-8
0.500
30o
1.2 x 10-7
0.659
41o

Step 4 - Test Your Understanding

Student drawings will vary. Check that the mirror is positioned so that the angle of incidence equals the angle of reflection and the reflected ray passes through the slit to be normal to the detector. The diffracted ray labeled 91 nm should make an angle of  30o with respect to the incident ray and the diffracted ray labeled 120 nm should make an angle of  41o with respect to the incident ray.