Focal Length of Convex Lens in Air

The focal length of a convex lens is a measure of its ability to converge or diverge light. In air, the focal length is given by the formula:

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

Where:
- f is the focal length in air
- n is the refractive index of the lens material
- R1 is the radius of curvature of the first surface of the lens
- R2 is the radius of curvature of the second surface of the lens

In this case, the focal length of the convex lens in air is given as 10 cm.

Finding the Refractive Index of the Liquid

To find the focal length of the lens when it is placed into a liquid with a refractive index of 1.75, we can rearrange the formula and solve for f:

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

Since the lens is placed into a liquid, we need to consider the refractive index of the liquid. Let's assume that the radius of curvature of both surfaces of the lens remains the same. Substitute the given values into the formula:

f = (1.75 - 1) * (1/R1 - 1/R2)

Now, let's calculate the new focal length.

Calculating the New Focal Length

Using the given refractive index of the liquid (n = 1.75), we can calculate the new focal length of the lens.

f = (1.75 - 1) * (1/R1 - 1/R2)

Since we don't have specific values for the radii of curvature of the lens surfaces, we cannot calculate the exact value of the new focal length. However, we can determine the relationship between the original focal length and the new focal length.

Relationship between Focal Lengths

The relationship between the focal lengths in air (f) and in the liquid (f') can be expressed as:

f' = nf

Where:
- f' is the new focal length of the lens in the liquid
- n is the refractive index of the liquid
- f is the original focal length of the lens in air

Substituting the given values into the equation, we have:

f' = 1.75 * 10 cm

Therefore, the new focal length of the convex lens when placed in the liquid with a refractive index of 1.75 is 17.5 cm.