A Ray of light in ait strikes a plane surface of a crown glass block at an angle of 50 degrees to the normal.
In what direction does the Ray travel through the glass block .
(Refractive index of glass=1.5)
What is the maximum angle of incidence for a Ray travelling from the glass block into air if the Ray is to Refract out of the block.
To determine the direction in which the light ray travels through the glass block, we need to use the laws of refraction. The first law of refraction, also known as Snell's law, states:
n1*sin(angle of incidence) = n2*sin(angle of refraction)
where n1 and n2 are the refractive indices of the initial and final mediums, and the angle of incidence is the angle between the incident ray and the normal to the surface.
In this case, the ray of light is traveling from air to a crown glass block. Since we are given the refractive index of glass (n2 = 1.5), and the angle of incidence is 50 degrees, we can rearrange Snell's law to solve for the angle of refraction:
sin(angle of refraction) = (n1/n2) * sin(angle of incidence)
Plugging in the known values, we have:
sin(angle of refraction) = (1/1.5) * sin(50 degrees)
sin(angle of refraction) ≈ 0.667 * 0.7660
sin(angle of refraction) ≈ 0.5116
To find the angle of refraction, we can take the inverse sine (also known as arcsine) of 0.5116:
angle of refraction ≈ arcsin(0.5116)
angle of refraction ≈ 30.3 degrees
Therefore, the light ray will travel through the glass block at an angle of approximately 30.3 degrees to the normal.
Now, let's determine the maximum angle of incidence for a ray traveling from the glass block into air in order for the ray to refract out of the block. To find this angle, we can use Snell's law again, but this time with the refractive indices reversed:
n2*sin(angle of refraction) = n1*sin(angle of incidence)
In this case, n1 is the refractive index of glass (1.5) and n2 is the refractive index of air (1.0). We want to find the maximum angle of incidence, so we need to find the critical angle where the angle of refraction is 90 degrees. We can rearrange Snell's law to solve for the maximum angle of incidence:
sin(angle of incidence) = (n2/n1) * sin(90 degrees)
Plugging in the known values, we have:
sin(angle of incidence) = (1.0/1.5) * 1
sin(angle of incidence) ≈ 0.667
To find the maximum angle of incidence, we can take the inverse sine of 0.667:
angle of incidence ≈ arcsin(0.667)
angle of incidence ≈ 41.8 degrees
Therefore, the maximum angle of incidence for a ray traveling from the glass block into air, in order for the ray to refract out of the block, is approximately 41.8 degrees.