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_{\mathrm{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 applies.
m={\frac{\theta}{\theta_{0}}}={\frac{25 \mathbf{cm}}{f}} (25.6)
(a) Find the maximum angular magnification of the lens.
Substitute into Equation 25.5:
m_{\text {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