A light beam containing red and violet wavelengths is incident on a slab of quartz at an angle of incidence of 50.0°. The index of refraction of quartz is 1.455 at 660 nm (red light), and its index of refraction is 1.468 at 410 nm (violet light). Find the dispersion of the slab, which is defined as the difference in the angles of refraction for the two wavelengths.
I understand I need to use n1*sin theta 1 equals n2 * sin theta 2.
But how do I get theta's from wavelength to put into the equation?
To find the dispersion of the slab, you need to calculate the angles of refraction for both red and violet light incident on the slab of quartz.
First, you can use the equation "n1 * sin(theta1) = n2 * sin(theta2)" to relate the angles of incidence and refraction, where n1 and n2 are the indices of refraction for the respective wavelengths of light and theta1 and theta2 are the angles of incidence and refraction, respectively.
To find the angles of incidence, you are given the angle of incidence (50.0°) in the problem statement.
To find the angles of refraction, you need to use Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction of the two media.
However, you are given the wavelengths of light (660 nm and 410 nm) instead of the angles, so you need to convert the wavelengths to angles using the equation "n * lambda = d * sin(theta)", where n is the index of refraction, lambda is the wavelength of light, d is the thickness of the slab, and theta is the angle of refraction.
To find the angles of refraction, you need to rearrange the equation and solve for the angle (theta). Rearranging gives you the equation "theta = arcsin(n * lambda / d)".
Using this equation, you can calculate the angles of refraction for both red and violet light by substituting the given values of the indices of refraction for quartz at each wavelength (1.455 for red light and 1.468 for violet light), the respective wavelengths (660 nm for red light and 410 nm for violet light), and any known values for the thickness of the slab.
Once you have the angles of refraction for both red and violet light, you can calculate the dispersion by subtracting the angle of refraction for red light from the angle of refraction for violet light.
Note: It is important to ensure that the angles are in the appropriate units (usually radians) when performing calculations, so you may need to convert degrees to radians if necessary.