A person with a myopic eye cannot see objects beyond 1.2 m distinctly. What should be the type and focal length of the c

Question

A person with a myopic eye cannot see objects beyond 1.2 m distinctly. What should be the type and focal length of the corrective lens used to restore proper vision?

Accepted Answer

Given: Far point of the myopic person, $v = -1.2	ext{ m} = -120	ext{ cm}$ Object distance for the far point, $u = -\infty$ Focal length of the lens, $f = ?$ 
Using the lens formula: $$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$ 
Substitute the given values into the formula: $$\frac{1}{f} = \frac{1}{-1.2} - \frac{1}{-\infty}$|
Since $\frac{1}{-\infty} = 0$: $$\frac{1}{f} = \frac{1}{-1.2}$$ $$f = -1.2	ext{ m} = -120	ext{ cm}$$ 
Power of the lens ($P$): $$P = \frac{1}{f	ext{ (in meters)}} = \frac{1}{-1.2} = -0.83	ext{ D}$| 
Conclusion:
The person is suffering from myopia (near-sightedness) and requires a concave lens of focal length $-1.2	ext{ m}$ (or $-120	ext{ cm}$) and power $-0.83	ext{ D}$ to correct this vision defect.

The Human Eye and Colourful World

❓ Sibling Questions in this Chapter