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Chapter 31: Problem 60

An object is \(28 \mathrm{cm}\) from a double-convex lens with \(n=1.5\) and curvature radii \(35 \mathrm{cm}\) and \(55 \mathrm{cm} .\) Where is the image, and what type is it?

Short Answer

Expert verified
Determine the exact values by substituting the given data into the formulas explained above. The sign of the image distance will tell you if the image is real or virtual. If the sign is negative, the image is a real image and located on the opposite side of the lens. If the sign is positive, it is a virtual image on the same side as the object.

Step by step solution

01

Understand and Interpret the Given Information

We have an object that is 28 cm from a double-convex lens with a refractive index (n) of 1.5 and curvature radii of 35 cm and 55 cm. We need to find out where the image will be formed, and whether it is real or virtual.
02

Use the Lensmaker's Equation to Find the Focal Length

The lensmaker's formula is given by \[ \frac{1}{f} = (n-1) ( \frac{1}{R1} - \frac{1}{R2}) \], where f is the focal length, n is the refractive index, R1 is the radius of curvature of the first lens surface and R2 is the radius of curvature of the second lens surface. Applying the values from the problem, we get \[ \frac{1}{f} = (1.5 - 1) ( \frac{1}{35} - \frac{1}{-55}) \]
03

Calculating the Focal Length

Calculate the value of f from the above expression. Remember that the radius of curvature for convex surface is considered as positive and for concave surface it is taken as negative
04

Use the Lens Formula to Determine Image Position

The lens formula is given by \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \], where f is the focal length, v is the image distance and u is the object distance. We know the object distance, u, is -28 cm (object distances are taken as negative), and we have calculated the focal length, f, in the previous step. We can substitute these values into the formula to find the image distance, v. If the image distance is a positive number, the image is virtual and on the same side of the lens as the object. If the image distance is negative, the image is real and on the opposite side of the lens.
05

Determine the Type of Image

From the sign of the image distance obtained in the previous step, you can determine whether the image is real or virtual.

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Most popular questions from this chapter

A double-convex lens with equal 28.5 -cm curvature radii is made from glass with refractive indices \(n_{\mathrm{red}}=1.512\) and \(n_{\text {violet }}=1.547 .\) If a point source of white light is located on the lens axis at \(75.0 \mathrm{cm}\) from the lens, over what distance will its visible image be smeared?

Show that identical objects placed equal distances on either side of the focal point of a concave mirror or converging lens produce images of equal size. Are the images of the same type?

Do you want a long or short focal length for a telescope's objective lens? What about a microscope's?

Is there any limit to the temperature you can achieve by focusing sunlight? (Hint: Think about the second law of thermodynamics.)

An object and its lens-produced real image are \(2.4 \mathrm{m}\) apart. If the lens has \(55-\mathrm{cm}\) focal length, what are the possible values for the object distance and magnification?
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