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 .To determine whether a frog can judge distance by means of the amount its lens must move to focus on an object, researchers covered one eye with an opaque material. An insect was placed in front of the frog, and the distance that the frog snapped its tongue out to catch the insect was measured with high-speed video. The experiment was repeated with a contact lens over the eye to determine whether the frog could correctly judge the distance under these conditions. If such an experiment is performed twice, once with a lens of power -9 D and once with a lens of power -15 D, in which case does the frog have to focus at a shorter distance, and why? (a) With the -9-D lens; because the lenses are diverging, the lens with the longer focal length creates an image that is closer to the frog. (b) With the -15-D lens; because the lenses are diverging, the lens with the shorter focal length creates an image that is closer to the frog. (c) With the -9-D lens; because the lenses are converging, the lens with the longer focal length creates a larger real image. (d) With the -15-D lens; because the lenses are converging, the lens with the shorter focal length creates a larger real image.

Short answer

The correct answer is (b), With the -15-D lens; because the lenses are diverging, the lens with the shorter focal length creates an image that is closer to the frog.

Step-by-step solution

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 $m^{-1}$.

Determine the true statement.

Since the power of the lens is inversely proportional to the distance of the image. The frogs need to focus at a shorter distance with -15-D lens as the lenses are diverging. The image created by the lens with a shorter focal length is closer to the frog.

Hence, with the -15-D lens; because the lenses are diverging, the lens with the shorter focal length creates an image that is closer to the frog.