Final answer:
To find the number of lines per centimeter on a diffraction grating, we can use the formula number of lines per centimeter = 1 / (distance between adjacent bright spots). Using the given angle of diffraction and wavelength of light, we can calculate the distance between adjacent bright spots and then the number of lines per centimeter. In this case, the number of lines per centimeter is approximately 5591.
Step-by-step explanation:
A diffraction grating is a device that contains many evenly spaced parallel slits or lines. When light passes through a diffraction grating, it diffracts into multiple beams due to constructive and destructive interference. The formula to calculate the number of lines per centimeter on a diffraction grating is:
Number of lines per centimeter = 1 / (distance between adjacent bright spots)
Using this formula, we can calculate the number of lines per centimeter for the given scenario. To find the distance between adjacent bright spots, we need to use the formula:
sin(theta) = (m * lambda) / d
where:
theta is the angle of diffraction (25.0° in this case)
m is the order of the maximum (1 for the first-order maximum)
lambda is the wavelength of light (470 nm)
d is the distance between the lines on the diffraction grating (to be calculated)
Plugging in the values:
sin(25.0°) = (1 * 470 nm) / d
d = (1 * 470 nm) / sin(25.0°)
d ≈ 1785 nm
Now we can use the formula to calculate the number of lines per centimeter:
Number of lines per centimeter = 1 / (d/10,000)
Number of lines per centimeter ≈ 1 / (1785 nm/10,000) ≈ 5591 lines/cm