A glass block has a refractive index of 1.49. What is the critical angle for the block?
sin^-1 (1/1.49)
To determine the critical angle for a glass block, we need to use Snell's law and the formula for the critical angle.
Snell's law relates the angles of incidence and refraction when light passes from one medium to another. It is given by:
n1 * sin(theta1) = n2 * sin(theta2)
Where:
- n1 is the refractive index of the first medium (in this case, the surrounding medium, such as air, which has a refractive index of approximately 1).
- theta1 is the angle of incidence (angle between the incident ray and the normal).
- n2 is the refractive index of the second medium (in this case, the glass block with a refractive index of 1.49).
- theta2 is the angle of refraction (angle between the refracted ray and the normal).
When the angle of refraction becomes 90 degrees (or sin(theta2) = 1), the light is refracted along the boundary between the two media. At this angle, the incident angle is called the critical angle (theta_c).
Therefore, we can rearrange Snell's law as follows:
n1 * sin(theta_c) = n2 * sin(90 degrees)
Since sin(90 degrees) = 1, the equation simplifies to:
n1 * sin(theta_c) = n2
Since n1 is approximately equal to 1 (for air), we can substitute this value:
1 * sin(theta_c) = 1.49
Rearranging the equation, we find:
sin(theta_c) = 1.49
To find the critical angle (theta_c), we need to take the inverse sine (or arcsine) of both sides of the equation:
theta_c = arcsin(1.49)
Using a calculator or mathematical software, we can find the arcsine of 1.49 to find the critical angle for the glass block.