Question

what is the focal length of a -7.75-diopter lens?
express your answer to three significant figures and include the appropriate units.
$f_2 = -0.129$ m
previous answers
correct
part c
are these lenses converging or diverging?
the first lens is converging, the second lens is diverging
the first lens is diverging, the second lens is converging
both lenses are converging
both lenses are diverging
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Explanation:

To determine if a lens is converging or diverging, we use the sign of the diopter (power, \( P \)) or focal length (\( f \)). The power of a lens is given by \( P=\frac{1}{f} \) (in meters). For a converging lens, the power is positive (and focal length is positive, as it converges light to a real focus on the other side of the lens). For a diverging lens, the power is negative (and focal length is negative, as it diverges light, and the focus is virtual, on the same side as the incoming light).

In the previous part, the second lens has a power of \(-7.75\) diopters (negative power), so its focal length is negative (as calculated: \(-0.129\) m). For the first lens (not shown here, but typically, if we consider the context of lens types), but since the second lens has negative power (diverging), and if we assume the first lens (if we had its power) – however, in the options, the key is the sign of power/focal length. Diverging lenses have negative power (and negative focal length), converging have positive. Since the second lens here has negative power (so diverging), and if we consider the first lens (even if not shown, but the options include "Both lenses are diverging" – wait, no, wait: Wait, the first lens? Wait, maybe in the original problem (not fully shown), but in the part C, the options: Wait, the second lens (from part A/B) has power \(-7.75\) D (diverging). If the first lens also has negative power (or focal length), then both are diverging. Wait, but let's recall: Diverging lenses have negative power (because \( P = 1/f \), and \( f \) is negative for diverging). So if a lens has negative power (negative focal length), it is diverging. So if both lenses (first and second) have negative power (or focal length), then both are diverging. So the correct option would be "Both lenses are diverging" (assuming the first lens also has negative power, which is consistent with the second lens here being negative).

Wait, but let's confirm: Converging lenses (like convex lenses) have positive power (positive \( f \)), diverging (concave) have negative power (negative \( f \)). So if a lens has negative power (or negative \( f \)), it's diverging. So if both lenses have negative power (or focal length), then both are diverging. So the correct option is "Both lenses are diverging".

Answer:

D. Both lenses are diverging