A narrow beam of light passes through a plate
of glass with thickness 1.4 cm and a refractive
index 1.55. The beam enters from air at an
angle 23.5 �. The goal is to calculate the
deviation d of the ray as indicated in the
figure.
To calculate the deviation, we need to find the angle of refraction of the light ray as it passes through the glass plate. We can use the Snell's law to relate the angles of incidence and refraction to the refractive indices of the two media (air and glass).
Snell's law 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 refractive indices of the two media. Mathematically, it can be written as:
n1 sin(theta1) = n2 sin(theta2)
Where:
- n1 is the refractive index of the first medium (air)
- theta1 is the angle of incidence
- n2 is the refractive index of the second medium (glass)
- theta2 is the angle of refraction
In this case, we are given:
- n1 (refractive index of air) = 1 (since air has a refractive index of approximately 1)
- theta1 (angle of incidence) = 23.5 degrees
- n2 (refractive index of glass) = 1.55 (given)
- We need to find theta2 (angle of refraction)
Using the values given, we can solve for theta2 using the Snell's law equation. Rearranging the equation, we have:
sin(theta2) = (n1/n2) * sin(theta1)
Plugging in the values:
sin(theta2) = (1/1.55) * sin(23.5)
Now, we can calculate the value of sin(theta2) using a calculator. Once we have the value, we can take the inverse sine (also known as arcsine) of that value to find the angle theta2.
Once we have the angle of refraction theta2, we can find the deviation d using the formula:
deviation d = (theta1 - theta2)
Substituting the values of theta1 and theta2 that we have calculated, we can find the value of deviation d.
Note: The figure mentioned in the question is not provided, so it is difficult to provide a specific calculation. However, this explanation should guide you to calculate the deviation once you have the necessary values.