Trace by drawing the path of a ray of light shown in 90 degrees. This ray is incident in a perpendicular direction on the figure through a glass triangular prism on one side of the right angle. Given that the two sides of the right angle are equals and that the critical angle between the glass and air is 42 degree. Find also the angle of emergence.

To trace the path of a ray of light through a glass triangular prism, and find the angle of emergence, follow these steps:

1. Draw a triangle representing the glass triangular prism, with one of the sides of the right angle horizontal and another side perpendicular to it.

2. Label the horizontal side as the base (let's call it AB), the vertical side as the height (let's call it AC), and the hypotenuse of the right angle as the prism's edge (let's call it BC).

3. Now, draw an incident ray coming from the left side of the prism towards the right side. This ray should be perpendicular to the base AB. Label the point where the incident ray hits the base AB as point D.

4. Measure the critical angle, which is the angle between the hypotenuse BC and the air outside the prism. According to the question, the critical angle is given as 42 degrees.

5. Since the critical angle is the angle of incidence for the light ray passing from the glass into the air, draw a ray entering the prism at point D, making an angle of 42 degrees with the normal to the surface. The normal is a line perpendicular to the surface of the prism at the point of incidence.

6. To determine the angle of refraction inside the prism, draw a line from point D, through the prism's vertical side, and extend it until it intersects the hypotenuse BC. Label this intersection point as E.

7. Measure the angle of refraction (angle between the normal and the refracted ray) inside the prism. According to Snell's Law, which governs the refraction of light, the angle of refraction can be calculated using the formula: sin(angle of incidence) / sin(angle of refraction) = refractive index (or index of refraction). The index of refraction of glass is typically around 1.5.

8. Calculate the angle of refraction using the information provided above. Rearrange the formula: sin(angle of refraction) = sin(angle of incidence) / refractive index. Then calculate the angle of refraction.

9. Finally, to find the angle of emergence, draw a line from point E to point C (the top corner of the prism opposite the base). Measure the angle between this line and the normal to the surface of the prism at point E. This angle is the angle of emergence.

By following these steps and using trigonometry and the laws of refraction, you can trace the path of the light ray and find the angle of emergence through the glass triangular prism.