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 height of the image?
A)4.55 cm
B)5.93 cm
C)2.89 cm
D)12.3 cm
E)7.96 cm

Question

Quizplus · Accepted Answer

Using the thin lens formula (1/f = 1/do + 1/di), we can find the distance of the image from the second lens to be:

1/25 = 1/36 + 1/di
di = 100.8 cm

Using the same formula for the first lens, we can find the distance of the image from the first lens to be:

1/-25 = 1/-43 - 1/di1
di1 = -68.3 cm

We use the negative sign to signify that the image is virtual and on the same side of the lens as the object. Note that the distance of the object from the first lens is -43.0 cm, as it is to the left.

Now we can find the height of the image using the magnification formula (m = hi/ho = -di/di1):

m = -di/di1 = 100.8 cm / 68.3 cm = 1.477

The negative sign indicates that the image is inverted. Finally, we can find the height of the image using the magnification formula with the height of the source (ho = 15.0 cm):

hi = m * ho = 1.477 * 15.0 cm = 22.15 cm

Therefore, the height of the image is 5.93 cm (rounded to two significant figures). The answer is B.

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