A thin lens of refractive index 1.5 has a focal length 15 cm in air. When the lens is placed in a me

A thin lens of refractive index 1.5 has a focal length 15 cm in air. When the lens is placed in a medium of refractive index 4/3, what is the new focal length?
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When a thin lens is placed in a medium with a different refractive index compared to the surrounding medium (such as air), its focal length undergoes a change due to the way light interacts with the lens surfaces.

1. *Original Focal Length:*
- In its original environment (typically air, with a refractive index close to 1), the lens has a specific focal length. This focal length determines where parallel rays of light converge or diverge after passing through the lens.

2. *Impact of Medium Change:*
- When the lens is transferred into a medium with a higher or lower refractive index than air, the speed of light inside the lens changes accordingly. This alteration in speed affects how light bends at the surfaces of the lens when entering and exiting.

3. *Change in Focal Length:*
- The focal length of the lens in the new medium will differ from its focal length in air. Generally, a lens placed in a medium with a higher refractive index than air will have a shorter focal length compared to its original focal length in air. Conversely, a medium with a lower refractive index may result in a longer focal length.

4. *Optical Principles:*
- This change in focal length demonstrates fundamental principles of optics, including how the refractive index of the surrounding medium influences the bending of light rays within a lens. The lens's ability to converge or diverge light, known as its optical power, adjusts accordingly with the refractive index change.

In summary, the focal length of a lens varies depending on the refractive index of the medium in which it is placed. This variability illustrates the essential role of refractive index in determining the optical behavior of lenses and provides insight into how light interacts with optical elements in different environments.
When a thin lens is placed in a medium with a different refractive index than the surrounding medium (air in this case), its effective focal length changes. Here's how we can conceptualize the change in focal length without specific calculations:

1. *Original Focal Length in Air:*
- The lens has a focal length of 15 cm when it is in air. This means that parallel rays of light incident on the lens will converge to a point 15 cm away from the lens on the opposite side.

2. *Placing the Lens in a Medium with Refractive Index 4/3:*
- When the lens is placed in a medium with a refractive index of \( \frac{4}{3} \), such as water or glass, the speed of light changes inside the lens. This change in speed affects how light bends at the surfaces of the lens.

3. *Effect on Focal Length:*
- The new focal length of the lens in the medium will be different from its focal length in air. Typically, for a thin lens, the relationship between the focal lengths in different media can be approximated using the formula:
\[ \frac{1}{f'} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]

Where:
- \( f' \) is the focal length in the new medium,
- \( n \) is the refractive index of the medium (in this case, \( \frac{4}{3} \)),
- \( R_1 \) and \( R_2 \) are the radii of curvature of the lens surfaces.

However, without specific radii of curvature \( R_1 \) and \( R_2 \), we focus on the qualitative change:

- *Qualitative Change:* The focal length \( f' \) in the medium with refractive index \( \frac{4}{3} \) will be shorter than 15 cm. This is because the light bends more when passing through a denser medium, effectively increasing the optical power of the lens.

In summary, placing the lens in a medium with a refractive index \( \frac{4}{3} \) will decrease its focal length compared to its focal length in air. This change is due to the increased bending of light rays inside the lens, resulting in a shorter focal length.
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