A 4.0 cm tall object is placed 8.0 cm in front of converging...

A 4.0 cm tall object is placed 8.0 cm in front of converging lens of focal length 10 cm. (a) Calculate the image distance. Use Lens equation, no credit for a ray diagram solution. (b) Calculate the image height. No credit for a ray diagram solution. (c) Draw a clear ray diagram to show the image formation mechanism (d) The image is i) upright ii) inverted iii) sideways iv) warped (e) The image is i) real ii) no image iii) virtual iv) complex (f) The size of the image (relative to the object) is i) magnified ii) same size iii) diminished

Transcript

00:01 So we have an object of four centimeters tall, placed eight centimeters in front of the converging lens, which has a focal length of 10 centimeters.

00:09 And first off, we want to find the image distance.

00:12 So we'll use our lens equation.

00:14 It says one over eight.

00:16 All the numbers here are understood to be in centimeters, plus one over the image distance.

00:21 We'll call it like s prime equals one over the focal length.

00:25 So, of course, one over s prime is equal to, 1 over the focal length minus 1 eighth.

00:34 The focal length, we're told is 10.

00:35 So just put that in here.

00:37 And so this is going to be a negative number.

00:40 So s prime is equal to negative 40 centimeters when we do the math here.

00:46 And so if we were to draw that, it would be somewhere over here.

00:53 So basically on the same side as the object.

00:57 And we'll get the scale and everything.

01:00 Correct in a moment but this is 40 centimeters away from our lens so let's draw that this is 40 centimeters and we want to know next up what is the image height so the to find the image height we need like the magnification so the magnification is negative h prime over h prime is the image height so the image height of course is negative m times h and m is going to be negative s prime over s where it's like the ratio of the image distance to the object distance.

01:37 So this is going to be negative times negative 40 over 8.

01:40 So just positive 5...

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