A ray of light goes through the centre of a semicircular glass disk, n = 1.58, and onto a wall (x = 19.4 cm, y = 5.06 cm). What is the incident angle, θ?
To find the incident angle (θ), we can use the laws of reflection which states that the angle of incidence is equal to the angle of reflection.
First, let's draw a diagram to visualize the situation:
```
|\
| \
θ | \
| \
|____\ (Wall)
O \
\
\
\ (Semicircular Glass Disk)
```
In the diagram, the semicircular glass disk is represented as a semicircle (O) and the wall is represented by a straight line (Wall). The incident ray of light passes through the center of the semicircle (O) and hits the wall at point P.
Now, we need to use the information provided to calculate the incident angle.
Given:
- Refractive index of the semicircular glass disk (n) = 1.58
- Coordinate of the point of impact on the wall (x, y) = (19.4 cm, 5.06 cm)
To calculate the incident angle (θ), we can use the formula:
θ = sin^(-1)((y - R) / R)
where R is the radius of the semicircular glass disk.
To find the radius (R) of the semicircular glass disk, we need to use the refractive index (n) which is related to the radius (R) by Snell's law:
n = sin(θ) / sin(90°)
sin(θ) = n * sin(90°)
θ = sin^(-1)(n)
Now, we can substitute the value of n to find the value of θ:
θ = sin^(-1)(1.58)
By evaluating this expression, we can find the value of θ, which will give us the incident angle of the ray of light passing through the center of the semicircular glass disk and hitting the wall.