Q109PP - University Physics with Modern Physics

Question

The eyes of amphibians such as frogs have a much flatter cornea but a more strongly curved (almost spherical) lens than do the eyes of air-dwelling mammals. In mammalian eyes, the shape (and therefore the focal length) of the lens changes to enable the eye to focus at different distances. In amphibian eyes, the shape of the lens doesn’t change. Amphibians focus on objects at different distances by using specialized muscles to move the lens closer to or farther from the retina, like the focusing mechanism of a camera. In air, most frogs are near-sighted; correcting the distance vision of a typical frog in air would require contact lenses with a power of about -6.0 D .What is the farthest distance at which a typical “near-sighted” frog can see clearly in air? (a) 12 m; (b) 6.0 m; (c) 80 cm (d) 17 cm.

Step-by-Step Solution

Answer

The correct answer is option (d), 17 cm.

Step 1: Define the focal length and Power of lens.

The focal length is the distance between the convex or concave mirror and the focal point of the mirror.

The relation between the distance of object $u$ , the distance of the image $u\text{'}$and the focal length $f$ is 

$\frac{1}{f}=\frac{1}{u}+\frac{1}{u\text{'}}$

The power of the lens is the inverse of its focal length $f$

$P=\frac{1}{f}$

Where $P$ is power in $m^{-1}$

Step 2: Determine the farthest distance of an object.

Given that,

$$\begin{gathered} u\text{'}=\infty \\ P=6 D \end{gathered}$$

The power of the lens is”

$$\begin{gathered} P=\frac{1}{u}+\frac{1}{u\text{'}} \\ 6=\frac{1}{u}-\frac{1}{\infty } \\ u=17 \mathrm{cm} \end{gathered}$$

Hence, the farthest distance at which a typical “near-sighted” frog can see clearly in air is 17 cm.