A concave spherical lens with radius of curvature of 0.2 m is filled with water.What is focal length of this lens system?Refractive index of water=4/3.Explain the ans.

To find the focal length of a concave spherical lens filled with water, we can use the lens maker's formula. This formula relates the focal length of a lens to its radii of curvature and the refractive indices of the materials involved. For a lens, the formula is given by:

Lens Maker's Formula

The lens maker's formula is expressed as:

1/f = (n - 1) * (1/R1 - 1/R2)

Where:

• f = focal length of the lens
• n = refractive index of the lens material relative to the surrounding medium
• R1 = radius of curvature of the first surface (positive for convex, negative for concave)
• R2 = radius of curvature of the second surface (positive for convex, negative for concave)

Parameters for Our Lens

In this case, we have a concave lens with the following parameters:

• Radius of curvature, R = 0.2 m (since it's concave, we take this as negative: R1 = -0.2 m)
• For a thin lens, R2 is also -0.2 m (assuming the lens is symmetric)
• Refractive index of water, n = 4/3

Calculating Focal Length

Now, substituting these values into the lens maker's formula:

1/f = (4/3 - 1) * (1/(-0.2) - 1/(-0.2))

First, simplify the refractive index:

4/3 - 1 = 1/3

Now, substituting this back into the equation:

1/f = (1/3) * (1/(-0.2) - 1/(-0.2))

Since both terms in the parentheses are equal, they cancel each other out:

1/f = (1/3) * (0)

This means:

1/f = 0

Thus, the focal length, f, approaches infinity. This indicates that the lens does not converge light rays to a point, which is characteristic of a concave lens.

Understanding the Result

The result we obtained shows that a concave lens diverges light rays rather than converging them. When filled with water, the lens's ability to diverge light remains unchanged, as the refractive index of water is less than that of glass or other materials typically used in lenses. This is why the focal length is effectively infinite, meaning that parallel rays of light will diverge as if they are coming from a point at infinity.

In summary, the focal length of a concave spherical lens filled with water is infinite, reflecting its nature to diverge light rather than focus it. This behavior is essential in applications such as eyeglasses for nearsightedness, where concave lenses are used to correct vision by diverging light rays before they enter the eye.

To determine the focal length of a concave spherical lens filled with water, we can use the lens maker's formula. This formula relates the focal length of a lens to its radii of curvature and the refractive indices of the materials involved. For a concave lens, the focal length will be negative, indicating that it diverges light.

Understanding the Lens Maker's Formula

The lens maker's formula is given by:

1/f = (n - 1) * (1/R1 - 1/R2)

Where:

• f = focal length of the lens
• n = refractive index of the lens material relative to the surrounding medium
• R1 = radius of curvature of the first surface (positive if convex, negative if concave)
• R2 = radius of curvature of the second surface (positive if convex, negative if concave)

Applying the Formula

In this case, we have a concave lens with a radius of curvature of 0.2 m. Since it is concave, we take R1 as -0.2 m. For a lens filled with water, we consider the refractive index of water (n = 4/3) and the surrounding medium, which is air (n = 1). Thus, the effective refractive index for our calculations becomes:

n = (4/3) / 1 = 4/3

For the second surface of the lens, we can assume it is also concave, and since we are dealing with a single surface, we can take R2 as -0.2 m as well. Now we can substitute these values into the lens maker's formula:

1/f = (4/3 - 1) * (1/(-0.2) - 1/(-0.2))

Calculating the Focal Length

First, simplify the expression:

1/f = (1/3) * (1/(-0.2) - 1/(-0.2))

Notice that both terms in the parentheses are equal, which means:

1/f = (1/3) * (0)

This results in:

1/f = 0

Thus, we find that:

f = ∞

Interpreting the Result

The focal length being infinite indicates that the lens does not converge light to a point; instead, it diverges light rays. This is characteristic of a concave lens, which always produces virtual images that are upright and smaller than the object. In practical terms, this means that the lens system, as described, does not have a real focal point where light converges.

In summary, the focal length of the concave spherical lens filled with water is infinite, reflecting its nature as a diverging lens. This understanding is crucial in optics, especially when designing systems that utilize lenses for various applications, such as cameras, glasses, and projectors.