A 40 cm tall object is placed 62 cm away from a converging...

A 4.0-cm tall object is placed 62 cm away from a converging lens of focal length 31 cm. What are the nature and location of the image? The image is virtual, 4.0 cm tall, and 62 cm from the lens on the same side as the object. virtual, 2.0 cm tall, and 15 cm from the lens on the side opposite the object. virtual, 2.5 cm tall, and 31 cm from the lens on the side opposite the object. real, 2.5 cm tall, and 31 cm from the lens on the same side as the object. real, 4.0 cm tall, and 62 cm from the lens on the side opposite the object.

Transcript

00:01 Okay, so we're given an object height of 4 centimeters, object distance of 62 centimeters, and a focal length of 31.

00:06 That is going to be positive with a converging lens.

00:10 We can use our lens equation to find the image distance, and this is going to give us some information.

00:17 You could treat this as a completely conceptual question, or you could treat it as a problem.

00:21 Let's do this as a problem.

00:23 So 1 over 31 is going to be equal to 1 over 62 plus 1 over d .i.

00:31 We're going to subtract 1 over 62 from both sides, and we're going to be left with 1 over d .i is equal 2.

00:40 So now use your calculator here, 1 divided by 31, minus 1 divided by 62, gives us 0 .01.

00:49 Hit the inverse button on your calculator, x to the negative 1, and that's going to give you an image distance of 62.

00:58 This is a special case for lenses.

01:02 We're right at the center of curvature here.

01:05 In other words, we're exactly two times the focal length.

01:09 So maybe you could have known this without using that equation, but i think it helps to get some confirmation with that.

01:15 And then we can also use the image height equation, or the magnification equation, h -i over h -o equals negative d -i over d -o.

01:25 Okay, so h -i is the image height, and that is an unknown for us.

01:30 The object height was 4, image distance is 62, and the object distance is 62.

01:40 So if we cross multiply here, we're going to get 62 h .i.

01:45 Is equal to negative 62 times 4.

01:49 And then we're going to divide by 62 on both sides.

01:53 So h .i.

01:54 Is going to be equal to negative 4.

01:58 Okay, so this gives us a lot of information to answer the question.

02:02 Let's look back at the choices here.

02:06 So first question is, is it real or virtual the image? well, just looking at the image distance, if you get a positive image distance, that's going to be a real image.

02:19 And if you get a negative image distance, that's going to be a virtual.

02:24 So the fact that we've got a positive here means we're going to have a real image for sure.

02:30 Okay.

02:30 And then the second question is, what's the location of it? well, if we look at the location, we figured out that it was 62 centimeters.

02:39 Now, again, positive or negative...

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