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Chapter 2: Problem 135

Find the focal length of a thin plano-convex lens. The front surface of this lens is flat, and the rear surface has a radius of curvature of \(R_{2}=-35 \mathrm{cm} .\) Assume that the index of refraction of the lens is \(1.5 .\)

Short Answer

Expert verified
The focal length of the plano-convex lens is \(-70 \mathrm{cm}\). The negative sign indicates that the lens is diverging.

Step by step solution

01

Insert the known values into the lensmaker's equation

We know that \(R_1 = \infty\), \(R_2 = -35 \mathrm{cm}\), and \(n = 1.5\). We can plug these values into the lensmaker's equation to find the focal length: \[ \frac{1}{f} = (1.5 - 1)\left(\frac{1}{\infty} - \frac{1}{-35 \mathrm{cm}}\right) \]
02

Simplify the fractions

Since \(\frac{1}{\infty}\) is negligible compared to other terms, we can simplify the equation to: \[ \frac{1}{f} = 0.5 \left(-\frac{1}{35 \mathrm{cm}}\right) \]
03

Solve for the focal length

To find the focal length, solve the equation for \(f\): \[ f = \frac{1}{0.5 \times (-\frac{1}{35 \mathrm{cm}})} \] Now, simplify the equation: \[ f = \frac{1}{-0.5 \times \frac{1}{35} \mathrm{cm^{-1}} } \] \[ f = \frac{35 \mathrm{cm}}{-0.5} \] \[ f = -70 \mathrm{cm} \]
04

Conclusion

The focal length of the plano-convex lens is \(-70 \mathrm{cm}\). The negative sign indicates that the lens is diverging.

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Most popular questions from this chapter

What is the focal length of a magnifying glass that produces a magnification of 3.00 when held \(5.00 \mathrm{cm}\) from an object, such as a rare coin?

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