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. A thin planoconvex lens with a radius of curvature of magnitude 28.0 $\mathrm{cm}$ on the curved face is made of silicate flint glass. (See Figure $23.29 . )$ When a colorful object is placed 65.0 $\mathrm{cm}$ from this lens, the yellow light of wavelength 550 $\mathrm{nm}$ is perfectly focused on a screen. (a) How far is the screen from the lens? (b) Where will red light of wavelength 700 $\mathrm{nm}$ and violet light of wavelength 400 $\mathrm{nm}$ be focused?

Violet image is formed in front of the screen at a distance of $140.54 \mathrm{cm}-122.14 \mathrm{cm}=12.4 \mathrm{cm}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 25

Optical Instruments

Electromagnetic Waves

Reflection and Refraction of Light

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

Lectures

02:30

In optics, ray optics is a geometric optics method that uses ray tracing to model the propagation of light through an optical system. As in all geometric optics methods, the ray optics model assumes that light travels in straight lines and that the index of refraction of the optical material remains constant throughout the system.

10:00

In optics, reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Reflection may also be referred to as "mirror image" or "specular reflection". Refraction is the change in direction of a wave due to a change in its speed. The refractive index of a material is a measure of its ability to change the direction of a wave. A material with a higher refractive index will change the direction of a wave to a greater degree than a material with a lower refractive index. When a wave crosses the boundary between two materials with different refractive indices, part of the wave is refracted; that is, it changes direction. The ratio of the speeds of propagation of the two waves determines the angle of refraction, which is the angle between the direction of the incident and the refractive rays.

09:28

A thin double-convex lens …

02:32

A thin planoconvex lens ha…

04:29

A double-convex lens with …

04:40

The radius of curvature of…

02:23

A magnifying glass is a si…

01:47

A microscope has an object…

00:50

$\bullet$ A converging len…

A glass lens with radii $r…

04:19

35.39. The radius of curva…

02:28

04:47

02:58

A thin lens with a focal l…

Okay, so let's take a look at the question one. So question was asking us. How far is the screen from the legs? So it's still painfully image distance, which is the value Me here, the V value. We know that one over advocacy with one overview. Plus, why were you? And while I have, it's also he goes to m minus one times. Well, over. I want minus one over house. Who so things both because it's evil. The one over half we'll get while we re possible. Over you. You go to M minus one times 1/1, minus 1/2. He is the image distance. New is the object distance and is the index of refraction. And I want is the radius of the curvature off the curve side of the plane comebacks There, okay. And are two is also the radius of curvature. Okay, in his case, are two is able to infinity things. The other service is a plane. Okay, so if we plug in the are to value, we'll get one of the three plus whatever you is equal in minus one times one with baba. While overall I minus one over infinity. And while the infinity is equal zero so that we'll get while Riverview cost, while real busy with M minus one times, whatever I want, Remember for question one we're looking for to find out the image. Distance the valley, which is give us Ah, this equipment you bus while reviews equal to minus one over our minus one over you. So long movies equals who, um, minus one task to you. Over. I'm sorry. Minus. I want over Utah's Allah Gov is equal to you Our over and minus one times U minus, Allah. Okay, so now we can clocking a value, remember, Use that the object isn't It is given 65 point. Oh, sending here. Okay. And I want these. Give us 28.7 years and ah, index over yellow lights. The refreshing over generalizes about 1.61 Okay, so now if you plug in a value or get Utah's our languages 65.7 years times 28 going 07 meters over oak. Uh, maybe you know what? Xcom kruky here on the war. Correct. Sorry about that. Okay, So Well, get on 65 going. Oh, centimeters times 28.7 years over 1.61 minus one times you. Which is 65.0, centimeters minus ah one, which is 28 going Oh, centimeters. Okay. And we get the image distance. It's about oh 1 40 going by four, seven years. Okay, the less the answer for question one. So will be how far it will be 140.54 centimeters from the screen to the lanes. Okay, so for question be it was asking us, uh, where we'll read lie and the violent lights be focused. Okay, so it's also telling about to find out the image distance. But in this time, we're focusing our another image distance or red line in the wild life. Okay, so you say, uh, being our he's the image distance for red line. Okay, that's a long we're looking for. And the the Levi, maybe he'll be here is the you live. This is what we want to be, too. So we want STV in a distant for rely and the me to is the British in for Well, we like and remember for on the last question we got B is equal to you, Awan. Over in minus one past U minus. I want. Okay, So and in his question I want which is the radius of courage Shirt is also is also equal to 28 point oh, seven meters. An object distance is still 65. Oh, sending the years. So the only difference between the red line any bar delights is just their index called refraction. Or let's focus on to find out the value off the image distant for rare lifers. So the index refraction for Lorella is given as end one equal to one point 61 Okay. And if we plug in, the value will give Be one is equal to youth has our wishes 65 going oh centimeters times 28 0.0, centimeters over M minus one was just in this case one point six y minus one times 65.0, seven meters minus 28.7 meters. And this will give us for you want This is now, huh? 156 0.2 seven years. Okay. And now in jumping to to figure out the image distance for the violent lights, which is we to be two is equal to you are one over and to which is the index of refraction of the wildly lights minus one past U minus. Our Okay, any index of refraction off the satellites is given us 1.6 six. Okay, boot. So if we plug in the value work every two, he's equal to 65.0 centimeters times. How long? Which is 28 0.0, centimeters over in two minus one, which is 1.66 minus one times you, which is 65.0, sending years minus 28.7 years. And this will give us the image distance off The violence is about 122 only 14 seven years. I remember, since these value is smaller than a distance between the object lands and screen. And the question was asking us, Ah, where will the red line in the borderline be focused? So seems the violently line that the value off the image distant revival image is smaller than a distant between screen in advance. We can say that a where the image is formed in front of the script as some kind of this is okay, which is? We use l to stand for the distance. Stempel, In front distance. We'll get our equal to V minus three, to which is remember V was given as 1 40 Pointing 54 centimeter. Okay. And then with minus the V two better, which is 122.14 centimeters. And this will give us the answer is 12.47 years. Okay, so

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