A small fish is inside a spherical bowl filled with water (n=1.33). The bowl has a diameter of 30cm and the fish is at a distance of 5cm from the surface that separates water and air (ignore the effects of the glass of the bowl). The image of the fish is ...
a. Real (forms in the air medium) and inverted
b. Real (forms in the air medium) and upright
c. Virtual (seems to form in the water) and inverted
d. Virtual (seems to form in the water) and upright
e. No image is formed due to Total Internal Reflection
To determine the nature of the image of the fish, we can use the concept of refraction.
When light passes from one medium to another with a different refractive index, it changes direction. In this case, the light would pass from water (refractive index = 1.33) to air (refractive index = 1.00).
The critical angle is the maximum angle at which light can pass from a more dense medium to a less dense medium without undergoing total internal reflection. Total internal reflection occurs when the angle of incidence exceeds the critical angle.
In this setup, the fish is closer to the air-water interface than the critical angle. Therefore, the light rays from the fish that travel towards the interface will be refracted out of the water and into the air.
Using the principle of refraction at a spherical interface, we can determine that the light rays will converge to form a real (forms in the air medium) and inverted image of the fish.
Therefore, the correct answer is:
a. Real (forms in the air medium) and inverted.
To determine the type and characteristics of the image of the fish inside the spherical bowl, we can use the concept of refraction of light at the water-air interface.
1. Determine the critical angle: The critical angle is the angle of incidence at which light bends to be parallel to the surface of separation between two media (in this case, water and air). It can be calculated using the refractive index of water (n = 1.33) according to the formula:
critical angle = arcsin(1/n)
So, the critical angle in this case would be arcsin(1/1.33) ≈ 48.8 degrees.
2. Determine the fish's angle of incidence: The angle of incidence is the angle at which light rays from the fish strike the water-air interface. Since the fish is 5cm away from the water-air surface and the bowl has a diameter of 30cm, the angle of incidence can be calculated using basic trigonometry:
angle of incidence = arctan(5/15) ≈ 18.4 degrees.
3. Compare the angles: If the angle of incidence is greater than the critical angle, total internal reflection occurs and no image is formed. However, if the angle of incidence is less than the critical angle, refraction occurs and an image is formed.
In this case, 18.4 degrees < 48.8 degrees, so total internal reflection does not occur.
Based on the above analysis, we can conclude that an image of the fish is formed inside the spherical bowl. To determine the characteristics of the image, we need to consider the refracted rays.
First, we note that the image is formed in the air medium because the rays travel from the water (where the fish is located) to the air (where the observer is positioned).
Since the image is formed by refraction and not reflection, it is a real image. Moreover, because the light rays pass through the focal point of the lens (the spherical bowl in this case), the image formed is inverted.
Therefore, the correct answer is:
a. Real (forms in the air medium) and inverted.