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Chapter 31: Problem 53

An object is \(68 \mathrm{cm}\) from a plano-convex lens whose curved side has curvature radius \(26 \mathrm{cm} .\) The refractive index of the lens is 1.62. Where is the image, and what type is it?

Short Answer

Expert verified
The calculation will provide the location and type of the image, which can be positive or negative. A positive image location indicates a real image, while a negative implies a virtual image.

Step by step solution

01

Calculation of Focal Length

Start with the lens maker's formula: \( \frac{1}{f} = (n - 1) \left[ \frac{1}{R_1} - \frac{1}{R_2} \right] \). \n For a plano-convex lens, one side is flat and the other side is curved. Hence \(R_1\) is infinity (\(\infty\)) and \(R_2\) is \(-26\) cm. The radius \(R_2\) is taken as negative as the center of curvature is on the other side of light incidence for a plano convex lens. The refractive index (\(n\)) is given as 1.62. Substitute the relevant values to find the focal length (\(f\)).
02

Get the Location of the Image

Next, apply the lens formula \( \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \) to find the position of the image (\(v\)). The object distance (\(u\)) is also given in the problem as -68 cm (the convention is to take distance on the side of light incidence as negative).
03

Determine the Image Type

The type of image (real or virtual) is determined by the sign of \(v\). If \(v\) is positive, it's a real image. If \(v\) is negative, it's a virtual image.

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Most popular questions from this chapter

The table below shows measurements of magnification versus object distance for a lens. Determine a quantity that, when you plot object distance against it, should give a straight line. Make your plot, establish a best-fit line, and use your line to find the focal length of the lens. $$\begin{array}{|l|c|c|c|c|c|}\hline \text { Object distance, } s(\mathrm{cm}) & 10.1 & 29.2 & 51.6 & 78.3 & 98.9 \\\\\hline \text { Magnification, } M & 1.31 & 4.77 & -4.38 & -1.27 & -0.724 \\\\\hline\end{array}$$

Under what circumstances will the image in a concave mirror be the same size as the object?

The cornea of the human eye has refractive index \(1.38,\) while the eye's lens has a graduated index in the range 1.38 to \(1.40 ;\) use 1.39 for this problem. For the aqueous humor between cornea and lens, \(n=1.34 .\) Find the angle through which light is deflected at the first surface of (a) the cornea and (b) the lens, if it's incident at \(20^{\circ}\) to the normal at each surface. Your result shows that the cornea is the dominant refractive element in the eye.

Can a concave mirror make a reduced real image? A reduced virtual image? An enlarged real image? An enlarged virtual image? Specify conditions for each possible image.

A lens has focal length \(f=35 \mathrm{cm} .\) Find the type and height of the image produced when a 2.2 -cm-high object is placed at distances (a) \(f+10 \mathrm{cm}\) and (b) \(f-10 \mathrm{cm} .\)
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