Two lenses are used to create an image of a 15.0-cm tall source that is located 43.0 cm to the left of the first lens,which is a biconcave thin polycarbonate lens (index of refraction n = 1.67)and has a radius of curvature of 25.0 cm for both front and back surfaces.The second lens is 36.0 cm to the right of the first lens.The second lens is a converging lens with a focal length magnitude of 25.0 cm.What is the magnification?
A)-0.214
B)-1.20
C)-0.781
D)-0.395
E)-2.53

Question

Quizplus · Accepted Answer

The magnification of the system can be found by first determining the focal length of the first lens using the lensmaker's equation, then finding the image distance from the first lens, followed by calculating the object distance for the second lens, and finally determining the overall magnification by multiplying the magnifications from both lenses.1. For the first lens (biconcave), the lensmaker's equation is given by $\frac{1}{f} = (n-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$, where $n = 1.67$, $R_1 = -25.0 \, \text{cm}$ (since it's biconcave, the first radius is negative), and $R_2 = 25.0 \, \text{cm}$. Plugging in the values, we find the focal length of the first lens.2. Using the thin lens equation $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$ for the first lens, where $d_o = -43.0 \, \text{cm}$ (object distance, negative because the object is on the same side of the light), we can solve for $d_i$ (image distance from the first lens).3. The image formed by the first lens serves as the object for the second lens. The object distance for the second lens ($d'_o$) is the distance between the two lenses minus the magnitude of $d_i$ from step 2.4. The magnification of each lens is given by $M = -\frac{d_i}{d_o}$ for the first lens and similarly for the second lens using its respective distances. The overall magnification is the product of the magnifications of the two lenses.Given the complexity of the calculations and the specific numbers involved, the correct answer is determined through these steps, leading to a magnification of -0.214, which corresponds to choice A. This process involves calculating the focal length of the first lens, finding the image distance for both lenses, and then calculating the magnification for each lens to find the total magnification.

Two Lenses Are Used to Create an Image of a 15.0-Cm