Spherical Lenses

diopter is a concave lens

Step 1: Thin lens formula.
The thin lens formula is given by: where is the focal length, is the image distance, and is the object distance.
Step 2: Sign convention for focal length.
For a concave lens (diverging lens), the focal length is negative.
For a convex lens (converging lens), the focal length is positive.

Step 3: Identify the correct option.
The correct option is (d) since concave lenses have a negative focal length.

Step 1: Power of the convex lens.
The power of a lens is given by the formula: where is the focal length in meters.
For the convex lens,
Step 2: Power of the diverging lens.
The power of the diverging lens is already given as (negative because it is a diverging lens).
Step 3: Total power of the combination.
The total power of the lens combination is the sum of the individual powers:
Step 4: Focal length of the combination.
The focal length of the combination is related to the total power by the formula: Substituting the total power:

Step 1: Understand the concept of focal length.
The focal length of a lens depends on the refractive index of the lens material relative to the surrounding medium.
The formula for focal length in terms of refractive index is: where is the refractive index of the lens and is the refractive index of the surrounding medium.
Step 2: Focal length in this case.
If the refractive index of the liquid is equal to the refractive index of the lens, the difference between and becomes zero.
As a result, the focal length becomes infinite, and the lens will no longer converge or diverge light.