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Chapter 31: Problem 49

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) \(f-10 \mathrm{cm} .\)

Short Answer

Expert verified
For the case (a) \(u=f+10cm\), the image distance will be positive and the image height will be negative which means the image is real and inverted. However, for the case (b) \(u=f-10cm\), both the image distance and image height will be negative, suggesting that the image produced will neither real nor inverted. It's virtual and inverted. The exact values of the image distance and image height will depend on the calculations in Step 2 and Step 3.

Step by step solution

01

Use the lens formula to find the image distance

The formula to find the image position, also called the lens formula, is \(1/f = 1/v - 1/u\), where \(f\) is the focal length, \(v\) is the image distance, and \(u\) is the object distance. Rearrange the equation in order to solve for \(v\) and then substitute the focal length \(f=35cm\) and object distance \(u=f+10cm\) and \(u=f-10cm\) for each respective case.
02

Calculate the image distance

Upon substituting the values of the focal length and object distance in the formula established in Step 1, the image distance can be computed for each case i.e., (a) and (b). This is the focal point of the image.
03

Use the magnification formula to find the height of the image

Magnification (\(m\)) is given by \(m = -v/u\). This gives the ratio of the height of the image (\(h_i\)) to the height of the object (\(h_o\)) so therefore the height of the image can be calculated by \(h_i = m \cdot h_o\). The negative sign denotes the orientation of the image. Hence, using the magnification formula, and the previously calculated image distance, along with the given object height, the height of the image can be calculated.
04

Determine the orientation of Image

If the magnification is negative, the image is said to be inverted with respect to the object, which means the image is real. If the magnification is positive, the image is upright with respect to the object, which means the image is virtual.

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Most popular questions from this chapter

You're given two lenses with different diameters. Knowing nothing else, you can conclude that a. the larger lens is faster. b. the smaller lens has the shorter focal length. c. the smaller lens suffers less spherical aberration. d. none of the above

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