Question

Which has more power: a thick convex lens or a thin convex lens, made of the same glass? Give reason for your choice.

Answer 1

Hint: In simple terms we will analyse what the power of the convex lens means and we will use the thickness of the lens to determine the focal length of the two lenses (the thick one and the thin one). With the help of the definition of power and focal length we will conclude the answer which one has more power.

Complete answer:
Power of the lens: The power of a lens is defined as the reciprocal of the focal length. Lens power is measured in dioptres (D). Convex lenses have positive focal lengths, so they also have positive power values. Concave lenses have negative focal lengths, so they also have negative power values.
$P={\displaystyle \frac{1}{f}}$
where $P$ is the power and $f$ is the focal length.

Now focal distance is the length of the focus from the centre of the lens. For a thick lens the focal distance will be less as compared to that of the thin lens. Since power is the reciprocal of focal length.The below diagram shows a thick and a thin lens.

Now,
$f_{thin}>f_{thick}$
Where $f_{thick}$ is the focal length of thick lens and $f_{thin}$ is the focal length of the thin lens
$\Rightarrow {\displaystyle \frac{1}{f_{thin}}}<{\displaystyle \frac{1}{f_{thick}}}$
Dividing changes, the sign of inequality
$\Rightarrow P_{thin}<P_{thick}$
Where $P_{thick}$ is the focal length of a thick lens and $P_{thin}$ is the focal length of the thin lens.

So, from the above derivation we conclude that the power of thick lens will be more than that of the power of thin lens.

Note:Here we are directly reciprocating the focal lengths by even considering the negative or positive signs of the focal length. If we consider the signs of the focal length then numerically for concave lens (negative sign) the power of a thick lens will be less than the power of a thin lens just the opposite of what we conclude in above. But for a convex lens the above solution holds true.