Question 25.3: MAGNIFICATION OF A LENS GOAL Compute magnifications of a len...
MAGNIFICATION OF A LENS
GOAL Compute magnifications of a lens when the image is at the near point and when it’s at infinity.
PROBLEM (a) What is the maximum angular magnification of a lens with a focal length of 10.0 \mathrm{~cm} ? (b) What is the angular magnification of this lens when the eye is relaxed? Assume an eye-lens distance of zero.
STRATEGY The maximum angular magnification occurs when the image formed by the lens is at the near point of the eye. Under these circumstances, Equation 25.5
m_{\max }=1+\frac{25 \mathrm{~cm}}{f} [25.5]
gives us the maximum angular magnification. In part (b) the eye is relaxed only if the image is at infinity, so Equation 25.6
m = \frac{\theta }{\theta _0} =\frac{25 \mathrm{~cm}}{f} [25.6]
applies.
(a) Find the maximum angular magnification of the lens.
Substitute into Equation 25.5:
m_{\max }=1+\frac{25 \mathrm{~cm}}{f}=1+\frac{25 \mathrm{~cm}}{10.0 \mathrm{~cm}}=3.5
(b) Find the magnification of the lens when the eye is relaxed.
When the eye is relaxed, the image is at infinity, so substitute into Equation 25.6:
m=\frac{25 \mathrm{~cm}}{f}=\frac{25 \mathrm{~cm}}{10.0 \mathrm{~cm}}=2.5