A index of certain type of glass has an an index of refraction of 1.66 for red light and 1.65 for violet light. If a beam of white in air approaches the glass with an angle of incidence of 49.0 degree, by what angle will the red light be separated from the violet light inside the glass?
For red, the sine of the refraction angle is
Sin49 /1.66
That comes from Snell's law, which you should know.
For violet, it is sin49/1.65
Compute the refraction angles using a sin^-1 function and take the difference.
To find the angle by which the red light and violet light separate inside the glass, we can use the concept of refraction and Snell's law.
1. Recall Snell's law, which relates the angles of incidence and refraction to the refractive indices of the media involved:
n1 * sin(theta1) = n2 * sin(theta2),
where n1 is the refractive index of the first medium, theta1 is the angle of incidence, n2 is the refractive index of the second medium, and theta2 is the angle of refraction.
2. In this case, the first medium is air with a refractive index of approximately 1 (since the refractive index of air is very close to 1), and the second medium is the glass with different refractive indices for red and violet light.
3. Let's calculate the angle of refraction for both red and violet light using Snell's law. For red light:
n_air * sin(theta_incident) = n_red * sin(theta_red),
where n_red is the refractive index of the glass for red light. Rearrange the equation to solve for sin(theta_red):
sin(theta_red) = (n_air * sin(theta_incident)) / n_red.
4. Similarly, for violet light:
n_air * sin(theta_incident) = n_violet * sin(theta_violet),
where n_violet is the refractive index of the glass for violet light. Rearranging the equation to solve for sin(theta_violet):
sin(theta_violet) = (n_air * sin(theta_incident)) / n_violet.
5. We can now find the angle by which the red light and violet light separate inside the glass by subtracting theta_red from theta_violet:
separation_angle = theta_violet - theta_red.
Now, let's calculate the values using the given information:
Given:
Angle of incidence (theta_incident) = 49.0 degree
Refractive index of glass for red light (n_red) = 1.66
Refractive index of glass for violet light (n_violet) = 1.65
Mathematical Steps:
1. Convert the angle of incidence from degrees to radians:
theta_incident = 49.0 * (pi/180) rad.
2. Calculate sin(theta_red):
sin(theta_red) = (1 * sin(theta_incident)) / 1.66.
3. Calculate sin(theta_violet):
sin(theta_violet) = (1 * sin(theta_incident)) / 1.65.
4. Calculate the angle by which the red light and violet light separate inside the glass:
separation_angle = theta_violet - theta_red.
Finally, let's calculate the separation angle:
theta_incident = 49.0 * (pi/180) = 0.85521 rad.
sin(theta_red) = (1 * sin(0.85521)) / 1.66 ≈ 0.31556.
sin(theta_violet) = (1 * sin(0.85521)) / 1.65 ≈ 0.31822.
separation_angle = theta_violet - theta_red ≈ 0.31822 - 0.31556 ≈ 0.00266 rad.
Therefore, the red light and violet light will separate by an angle of approximately 0.00266 radians when passing through the glass.