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 determine the angle of refraction when light passes from air to water, you can use the formula known as Snell's Law:
n1 * sin(angle1) = n2 * sin(angle2)
Where:
- n1 is the refractive index of the initial medium (air in this case)
- angle1 is the angle of incidence (which is given as 45.0 degrees to the normal)
- n2 is the refractive index of the final medium (water in this case)
- angle2 is the angle of refraction (which we need to find)
Plugging in the given values, we have:
1 * sin(45.0 degrees) = 1.33 * sin(angle2)
Now, we need to solve for angle2. Rearranging the equation, we get:
sin(angle2) = (1 * sin(45.0 degrees)) / 1.33
Taking the inverse sine of both sides, we find:
angle2 = sin^(-1)[(1 * sin(45.0 degrees)) / 1.33]
Using a calculator, the value of angle2 is approximately 32.1 degrees.
Therefore, the correct answer is option B, 32.1 degrees.
Now, let's move on to the second question:
To determine the nature of the image formed by a concave mirror, you can use the mirror formula:
1/f = 1/u + 1/v
Where:
- f is the focal length of the mirror (given as 10 cm)
- u is the object distance (given as 3 cm)
- v is the image distance (which we need to determine the nature of the image)
Plugging in the given values, we have:
1/10 = 1/3 + 1/v
Now, we need to solve for v. Rearranging the equation, we get:
1/v = 1/10 - 1/3
Combining the fractions, we have:
1/v = (3 - 10) / (10 * 3)
Simplifying further, we get:
1/v = -7 / 30
Taking the reciprocal of both sides, we find:
v = -30 / 7
Since the image distance (v) is negative, it indicates that the image formed by the concave mirror is virtual.
Therefore, the correct answer is option C, virtual and inverted.