1. A grating containing 4000 slits per centimeter is illuminated with a monochromatic light and produces the second-order bright line at a 30° angle. What is the wavelength of the light used? (1 Å = 10-10 m)
Known :
The distance between slits (d) = 1 / (4000 slits / cm) = 0.00025 cm = 2.5 x 10-4 cm = 2.5 x 10-6 meters
Order (n) = 2
Sin 30o = 0.5
1 Å = 10-10 m
Wanted: Wavelength of the light (λ)
Solution :
[irp]
2. A monochromatic light with a wavelength of 2.5x10-7 m strikes a grating containing 10,000 slits/cm. Determine the angular positions of the second-order bright line.
Known :
The distance between slits (d) = 1 / (10,000 slits / cm) = 0.0001 cm = 1 x 10-4 cm = 1 x 10-6 m
Order (n) = 2
Wavelength (λ) = 2.5 x 10-7 m
Wanted : Angle (θ)
Solution :
[irp]
3. A monochromatic light with wavelength of 5.10-7 m strikes a grating. Distance between slit and the viewing screen is 2 m, distance between the third-order fringe and the central fringe is 150 cm. Determine distance between slits.
Known :
Wavelength (λ) = 5 x 10-7 m
l = 2 m
n = 3
y = 150 cm = 1.5 m
Wanted : distance between slits
Solution :
sin θ ≈ tan θ = y / l = 1.5 / 2 = 0.75 = 75 x 10-2
Distance between slits :
d sin θ = n λ
d (75.10-2) = (3)(5.10-7)
d (75.10-2) = 15.10-7
d = (15.10-7) / (75.10-2)
d = (15/75).10-5
d = (1/5)(10-5) m
d = (0.2)(10-5) m
d = 2.10-6 m
4. A monochromatic light with wavelength of 500 nm (1 nano = 10-9) strikes a grating and produces the fourth-order bright line at an 30° angle. Determine the number of slits per centimeter.
Known :
Wavelength (λ) = 500.10-9 m = 5.10-7 m
θ = 30o
n = 4
Wanted : number of slits per centimeter
Solution :
Distance between slits :
d sin θ = n λ
d (sin 30o) = (4)(5.10-7)
d (0.5) = 20.10-7
d = (20.10-7) / 0.5
d = 40.10-7
d = 4.10-6 m
Number of slits per centimeter :
x = 1 / 4.10-6 m
x = 0.25.106 / m
x = 0.25.106 / 102 cm
x = 0.25.104 / cm
x = 25.102 / cm
x = 2500 / cm
5. A monochromatic light with wavelength of 500 nm (1 nm = 10-9 m) strikes a grating and produces the second-order bright line at an 30° angle. Determine the number of slits per centimeter.
Known :
Wavelength (λ) = 500.10-9 m = 5.10-7 m
θ = 30o
n = 2
Wanted : number of slits per centimeter
Solution :
Distance between slits :
d sin θ = n λ
d (sin 30o) = (2)(5.10-7)
d (0.5) = 10.10-7
d = (10.10-7) / 0.5
d = 20.10-7
d = 2.10-6 m
Number of slits per centimeter :
x = 1 / d
x = 1 / 2.10-6 m
x = 0.5.106 / 1 m
x = 0.5.106 / 102 cm
x = 0.5.104 / cm
x = 5.103 / cm
x = 5000 / cm
