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 and position of the image of the fish, we can use the concepts of refraction and image formation.
When light travels from one medium to another, it bends or refracts due to the change in speed. The amount of refraction depends on the refractive indices of the two media.
In this case, we have a small fish inside a spherical bowl filled with water (n=1.33). The fish is at a distance of 5cm from the surface that separates water and air.
Since the fish is in water and the light rays are entering from water to air, the light rays will bend away from the normal as they move from a higher refractive index (water) to a lower refractive index (air).
Using the concept of refraction at a plane surface, we can draw the refracted ray backwards to find the path of the rays after they leave the water.
In this case, since the rays bend away from the normal, they will propagate in such a way that they appear to come from a virtual point below the water surface. Therefore, the image of the fish will be virtual and seem to form in the water.
Now, let's consider the orientation of the image. As the rays of light pass through the surface of the water, they undergo inversion due to the change in the refractive index. This means that the image will be inverted.
Therefore, the correct answer is:
c. Virtual (seems to form in the water) and inverted.
To determine the type and characteristics of the image formed by the fish, we need to consider the properties of refraction and the position of the fish relative to the surface separating water and air.
1. Start by drawing a diagram of the situation. Draw a horizontal line to represent the water-air interface. Place the fish below this line, 5cm away from it.
2. Given that the fish is inside a spherical bowl filled with water, we know that light rays will undergo refraction as they pass through the water-air interface.
3. Now, let's consider the different possibilities:
a. Real (forms in the air medium) and inverted: This option suggests that light rays from the fish enter the air medium and form a real, inverted image. For this to occur, the light rays must bend at the water-air interface such that they converge. However, this is not possible in this case, as the fish is positioned below the water-air interface. Therefore, we can eliminate this option.
b. Real (forms in the air medium) and upright: Similar to option a, this option suggests that light rays from the fish enter the air medium, but the image formed would be upright instead of inverted. Again, this is not possible given the fish's position below the water-air interface. Therefore, we can eliminate this option as well.
c. Virtual (seems to form in the water) and inverted: In this case, the light rays from the fish would bend at the water-air interface, but they would not actually enter the air medium. Instead, they appear to originate from a position behind the fish when traced backward. This virtual image would also be inverted compared to the actual fish. This option seems plausible given the fish's position, so let's keep it for further consideration.
d. Virtual (seems to form in the water) and upright: Similar to option c, this option suggests a virtual image forming in the water. However, it contradicts the fish's physical position below the water-air interface. Hence, we can eliminate this option.
e. No image is formed due to Total Internal Reflection: Total Internal Reflection occurs when light rays encounter an interface with a higher refractive index (in this case, water) from a medium with a lower refractive index (in this case, air) at an angle larger than the critical angle. However, there is no mention of any reflective condition or specific angles in the given scenario. Thus, we can eliminate this option.
Based on the analysis above, option c, "Virtual (seems to form in the water) and inverted," is the most appropriate answer.