Optics Image Formation by Refracting Surfaces

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1 Otics Image Formation by Refracting Surfaces Lana Sheridan De Anza College June 11, 2018

2 Last time images formed by sherical mirrors refracting surfaces

3 Overview images formed by refraction lenses

4 Images Formed by Refraction + n 2 q = n 2 R

5 Flat Refracting Surfaces (Like a rectangular fish tank.) 1102 Chater 36 Image Formation The image is virtual and on the same side of the surface as the object. O n 2 n 2 Figure The image formed q Flat Refracting Surfaces If a refracting surface is flat, then R is infinite an In this case R. 52n 2 q + n 2 q = 0 q 52 n 2 From this exression, And so we see that the sign of q according to Table 36.2, the image formed by a same side of the surface q as = the n 2 object n as illustrate 1 in which the object is in the medium of index case, a virtual image is formed between the objec n 2, the rays on the back side diverge from one an in Figure As a result, the virtual image is fo Q uick Quiz 36.4 In Figure 36.16, what haens oint O is moved to the right from very far awa

6 Flat Refracting Surfaces Examle (Problem 30) A cubical block of ice 50.0 cm on a side is laced over a seck of dust on a level floor. Find the location of the image of the seck as viewed from above. The index of refraction of ice is

7 Flat Refracting Surfaces Examle (Problem 30) A cubical block of ice 50.0 cm on a side is laced over a seck of dust on a level floor. Find the location of the image of the seck as viewed from above. The index of refraction of ice is n 2 q = n 2 R, R q = n 2

8 Flat Refracting Surfaces Examle (Problem 30) A cubical block of ice 50.0 cm on a side is laced over a seck of dust on a level floor. Find the location of the image of the seck as viewed from above. The index of refraction of ice is n 2 q = n 2 R, R q = n 2 = 1 (50.0 cm) = 38.2 cm The image will aear 38.2 cm below the surface of the ice.

9 Sign Conventions for Refracting Surfaces! + n 2 q = n 2 R Variable is Positive is Negative object in front of surface [virtual object] 1 q image behind surface image in front of surface (real) (virtual) h (and M) image uright image inverted R object faces convex surf. object faces concave surf. (C behind surface) (C in front of surface) C is the center of curvature. M = h h = q n 2 1 Will be useful in derivations.

10 Refracting Surface Question Quick Quiz 36.4 In the figure, what haens to the image oint I Rays making small angles with the as the object oint O is moved to the rightrincial from very axis diverge far away from a oint to very close to the refracting surface? (A) It is always to the right of the surface. (B) It is always to the left of the surface. (C) It starts off to the left, and at some osition of O, I moves to the right of the surface. (D) It starts off to the right, and at some osition of O, I moves to the left of the surface. object at O and are refracted through the image oint I. O n 2 n 2 Figure An image formed by refraction at a sherical surface. q R I 36 In t und side bou We Let at th F law Bec tion We inte 1 Serway & Jewett, age 1102.

11 Refracting Surface Question Quick Quiz 36.4 In the figure, what haens to the image oint I Rays making small angles with the as the object oint O is moved to the rightrincial from very axis diverge far away from a oint to very close to the refracting surface? (A) It is always to the right of the surface. (B) It is always to the left of the surface. (C) It starts off to the left, and at some osition of O, I moves to the right of the surface. (D) It starts off to the right, and at some osition of O, I moves to the left of the surface. object at O and are refracted through the image oint I. O n 2 n 2 Figure An image formed by refraction at a sherical surface. q R I 36 In t und side bou We Let at th F law Bec tion We inte 1 Serway & Jewett, age 1102.

12 Refracting Surface Question 1102 Chater 36 Image For Quick Quiz 36.5 In the figure, what haens The image to the is virtual image and on oint I the same side of the surface as the object oint O moves toward the right-hand as the object. surface of the material of index of refraction? (A) It always remains between O and the surface, arriving at the surface just as O does. (B) It moves toward the surface more slowly than O so that eventually O asses I. (C) It aroaches the surface and then moves to the right of the surface. 1 Serway & Jewett, age O n 2 n 2 Figure The image formed by a flat refracting surface. All rays are assumed to be araxial. q Flat If a r From acco same in wh case, n 2, t in Fi Q ui o su th rig

13 Refracting Surface Question 1102 Chater 36 Image For Quick Quiz 36.5 In the figure, what haens The image to the is virtual image and on oint I the same side of the surface as the object oint O moves toward the right-hand as the object. surface of the material of index of refraction? (A) It always remains between O and the surface, arriving at the surface just as O does. (B) It moves toward the surface more slowly than O so that eventually O asses I. (C) It aroaches the surface and then moves to the right of the surface. 1 Serway & Jewett, age O n 2 n 2 Figure The image formed by a flat refracting surface. All rays are assumed to be araxial. q Flat If a r From acco same in wh case, n 2, t in Fi Q ui o su th rig

14 t of me, is flat yes. lowin car rva- 15). ind our oes changes according to Snell s law, sin u 1 5 n 2 sin u 2. For araxial rays, we assume u 1 and u 2 are small, so we A curved may refracting write n surface searates a material with index of 1 tan u 1 5 n 2 tan u 2. The magnification is refraction defined from as M a material 5 h9/h. with Prove index that n 2 the. Prove magnification that the is magnification is given by M = q given by M 5 2 q/n 2. Refracting Surface Examle (Problem 34) rolose an tual h O n 2. n 2 u 1 u 2 q C Figure P A glass shere (n ) with a radius of 15.0 cm has a M tiny air bubble 5.00 cm above its center. The shere is viewed looking down along the extended radius containing the bubble. What is the aarent deth of the bubble below the surface of the shere? I h

15 t of me, is flat yes. lowin car rva- 15). ind our oes changes according to Snell s law, sin u 1 5 n 2 sin u 2. For araxial rays, we assume u 1 and u 2 are small, so we A curved may refracting write n surface searates a material with index of 1 tan u 1 5 n 2 tan u 2. The magnification is refraction defined from as M a material 5 h9/h. with Prove index that n 2 the. Prove magnification that the is magnification is given by M = q given by M 5 2 q/n 2. Refracting Surface Examle (Problem 34) rolose an tual h O n 2. n 2 u 1 Hint: For araxial rays, wefigure assumep36.34 θ 1 and θ 2 are small, so we may write 35. Snell s A glass Law shere as (n tan 5 θ1.50) 1 = n 2 with tan θa 2 radius. of 15.0 cm has a M tiny air bubble 5.00 cm above its center. The shere is viewed looking down along the extended radius containing the bubble. What is the aarent deth of the bubble below the surface of the shere? u 2 q C I h

16 t of me, is flat yes. lowin car rva- 15). ind our oes changes according to Snell s law, sin u 1 5 n 2 sin u 2. For araxial rays, we assume u 1 and u 2 are small, so we A curved may refracting write n surface searates a material with index of 1 tan u 1 5 n 2 tan u 2. The magnification is refraction defined from as M a material 5 h9/h. with Prove index that n 2 the. Prove magnification that the is magnification is given by M = q given by M 5 2 q/n 2. Refracting Surface Examle (Problem 34) rolose an tual h O n 2. n 2 u 1 u 2 Hint: For araxial rays, wefigure assumep36.34 θ 1 and θ 2 are small, so we may write 35. Snell s A glass Law shere as (n tan 5 θ1.50) 1 = n 2 with tan θa 2 radius. of 15.0 cm has a ForMsmall tiny angles: air bubble 5.00 cm above its center. The shere is viewed looking down along the extended radius containing 1 tan θ n the 1 = n bubble. 2 tan θ What 2 is the aarent deth of the bubble below h the surface ( h ) = n 2 of the M shere? = h q h = q n 2 q C I h

17 Images Formed by Thin Lenses We will derive the thin lens equation 1 f = q (Notice it is the same as the mirror equation!) And the lens maker s equation 1 f ( 1 = (n 1) 1 ) R 1 R 2 We do this by considering each side of the lens as a refracting surface.

18 Summary images formed by refraction lenses Collected Homework! due Monday, June 18. Final Exam 9:15-11:15am, Tuesday, June 26. Homework Serway & Jewett: Carefully read all of Chater 36. Ch 36, onward from age OQs: 1, 3, 5, 11; CQs: 5, 9, 11; Probs: 39, 43, 53, 71