Light passes from air into water at 45.0 degrees to the normal. If the index of refraction of water is 1.33, find the angle of refraction.
A. 25.5 degrees
B. 32.1 degrees
C. 44.0 degrees
D. 55.9 degrees
I believe it is B?
What is the nature of an image formed by a concave mirror of focal length 10 cm for a real object placed 3 cm from the mirror?
A. Real and inverted
B. Real and upright
C. Virtual and inverted
D. Virtual and upright
I think this one is D?
To find the angle of refraction, we can use Snell's law, which 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 indices of refraction of the two mediums. Mathematically, it can be written as:
sin(angle of incidence) / sin(angle of refraction) = index of refraction of first medium / index of refraction of second medium
In this case, the angle of incidence is given as 45.0 degrees and the index of refraction of water is given as 1.33. We need to find the angle of refraction.
Let's plug in the values into the equation and solve for the angle of refraction.
sin(45.0 degrees) / sin(angle of refraction) = 1 / 1.33
sin(angle of refraction) = sin(45.0 degrees) / 1.33
Now we can take the inverse sine of both sides to find the angle of refraction.
angle of refraction = arcsin(sin(45.0 degrees) / 1.33)
Using a calculator to evaluate the above expression, we get angle of refraction ≈ 32.1 degrees.
Therefore, the correct answer is B. 32.1 degrees.
For the second question, the nature of the image formed by a concave mirror can be determined using two rules:
1. If the object is placed between the focal point (F) and the mirror, the image formed is virtual, upright, and enlarged.
2. If the object is placed beyond the focal point (F), the image formed is real, inverted, and diminished.
In this question, the object is placed 3 cm from the mirror which is closer to the mirror than the focal point (F). Therefore, according to the first rule, the image formed is virtual, upright, and enlarged.
Therefore, the correct answer is C. Virtual and upright.