A concave, spherical mirror and a thin, converging lens are both measured in air (n=1.0) to have the same focal length, ff. Both the mirror and the lens are then placed under water (n=1.33) and their focal lengths are measured again.
For both the mirror and the lens state whether its focal length under water will be the same, longer or shorter than ff and in both cases give a reason for your answer.
the focal length of the concave mirror stays the same.
The focal length of the converging lens gets shorter.
the index of refraction is not a factor in the concave mirror's focal point. However, it is a factor in the converging lens' focal point, as seen in the Lens Maker's Equation, or Snell's law.
Well, well, well! We have a concave, spherical mirror and a thin, converging lens measuring their focal lengths in air and then in water. Let's dive into it!
For the concave mirror, its focal length under water will be shorter than in air. Why you ask? Well, when the mirror is submerged in water (n=1.33), its speed decreases compared to when it's in air (n=1.00). As a result, the light rays that hit the mirror bend more as they pass through the water, causing the focal length to decrease.
Now, let's talk about the thin, converging lens. Its focal length under water will also be shorter than in air. Why, you wonder? Similar to the mirror, when the lens is immersed in water (n=1.33), the speed of light slows down. This change in speed causes the light rays to bend more as they pass through the water, resulting in a shorter focal length.
So, in both cases, the focal lengths under water will be shorter. The moral of the story is that when it comes to water, mirrors and lenses just can't handle the pressure and end up "short-sighted." It's a tough world underwater, my friend!
For a concave, spherical mirror and a thin, converging lens, when they are measured in air (n=1.0) and have the same focal length (ff), their behavior will change when placed under water (n=1.33).
1. Concave Spherical Mirror:
When a concave, spherical mirror is placed under water (n=1.33), its focal length will become shorter than ff.
Reason:
The refractive index of water is higher than that of air. When light passes from a medium with a lower refractive index (air) to a medium with a higher refractive index (water), it bends towards the normal. This means that the light rays traveling from air into water will bend towards the mirror. This results in a smaller angle of incidence, causing the reflected rays to diverge more, and the focal length of the mirror becomes shorter.
2. Thin, Converging Lens:
When a thin, converging lens is placed under water (n=1.33), its focal length will become longer than ff.
Reason:
Similar to the concave, spherical mirror, the refractive index of water is higher than that of air. When light passes from air to water, it bends towards the normal. For a converging lens, this means that the light rays entering the lens will bend towards its optical axis. This causes the rays to converge less, resulting in a longer focal length for the lens when placed in water.
To determine the focal lengths of the concave, spherical mirror and converging lens under water, we need to consider the relationship between the refractive index, the focal length, and the medium in which the object is placed.
When light passes through different mediums, its speed changes, resulting in a change in the direction of light rays. This change in direction is what causes the bending of light, known as refraction. The refractive index, denoted by "n," is a measure of how much a medium slows down the speed of light compared to its speed in a vacuum.
In this case, the refractive index of air is 1.0, and the refractive index of water is 1.33.
1. Concave, spherical mirror:
The focal length of a mirror is determined by the curvature of its surface. When the mirror is placed under water (higher refractive index), the speed of light decreases, causing light rays to bend more. As a result, the focal length under water will be shorter compared to the focal length in air. This is because the change in refractive index causes more refraction and increases the convergence of light rays.
2. Converging lens:
The focal length of a lens depends on its shape and the refractive index of the medium. In this case, as the converging lens is placed under water (higher refractive index), the speed of light decreases, causing light rays to bend more. The change in refractive index results in increased refraction compared to the refractive index in air. Consequently, the focal length of the lens under water will also be shorter compared to the focal length in air, as more convergence of light rays occurs due to the increased refraction.
In summary, both the concave, spherical mirror and the converging lens will have shorter focal lengths when placed under water compared to their focal lengths in air. This is because the higher refractive index of water causes increased refraction, resulting in more converging of light rays and a shorter focal length.