7C%20S03%20Bk%2015%20Exercises%20and%20Q-Ps

# 7C%20S03%20Bk%2015%20Exercises%20and%20Q-Ps - P h y s i c s...

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Unformatted text preview: P h y s i c s 7 C S p r i n g 2 3 : B l o c k 1 5 E x e r c i s e s & Q / P s 1 3 3 2 E x a m p l e s 1 . C a l c u l a t e a n d d e s c r i b e t h e r e f r a c t i o n o f a l i g h t r a y i n c i d e n t a t 4 5 ° f r o m t h e n o r m a l o n a t h i n l a y e r o f w a t e r o n t o p o f a h o r i z o n t a l s h e e t o f g l a s s . S o l u t i o n W e f i r s t u s e S n e l l ' s L a w a t t h e f i r s t i n t e r f a c e b e t w e e n a i r ( m e d i u m 1 ) a n d w a t e r ( m e d i u m 2 ) , t o f i n d t h e a n g l e o f t h e r e f r a c t e d l i g h t r a y i n w a t e r : n 1 s i n θ 1 = n 2 s i n θ 2 , θ 2 = A r c s i n n 1 s i n θ 1 n 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = A r c s i n 1 ( ) s i n 4 5 ° 1 . 3 2 9 ( ) ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = 3 2 . 1 4 ° . B y i n s p e c t i o n o f t h e g e o m e t r y i n v o l v e d , t h i s i s a l s o t h e a n g l e o f i n c i d e n c e a t t h e i n t e r f a c e b e t w e e n w a t e r ( m e d i u m 2 ) a n d g l a s s ( m e d i u m 3 ) : n 2 s i n θ 2 = n 3 s i n θ 3 , θ 3 = A r c s i n n 2 s i n θ 2 n 3 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = A r c s i n 1 . 3 2 9 ( ) s i n 3 2 . 1 4 ° 1 . 5 2 ( ) ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = 2 7 . 7 2 ° . N o t e t h a t t h e a n g l e i n t h e h i g h e r n m e d i u m i s a l w a y s s m a l l e r . 2 . A n o b j e c t 1 c m h i g h i s l o c a t e d 7 c m a w a y f r o m a f = + 3 c m l e n s . ( a ) L o c a t e t h e i m a g e , w i t h r e s p e c t t o t h e l e n s . ( b ) H o w l a r g e ( i n c m ) i s t h i s i m a g e ? S o l u t i o n T h i s i s a s t r a i g h t f o r w a r d a p p l i c a t i o n o f t h e t h i n l e n s e q u a t i o n . S i n c e w e a r e g i v e n t h e o b j e c t d i s t a n c e o a n d f o c a l l e n g t h f , w e c a n s o l v e f o r t h e i m a g e d i s t a n c e i — a s l o n g a s w e c a r e f u l a b o u t t h e r e c i p r o c a l a r i t h m e t i c i n t h e t h i n l e n s e q u a t i o n : 1 o + 1 i = 1 f , 1 i = 1 f − 1 o = o − f f o , i = f o o − f = + 3 c m ( ) 7 c m ( ) 7 c m ( ) − + 3 c m ( ) = + 5 . 2 5 c m . S i n c e t h e i m a g e d i s t a n c e i s p o s i t i v e , t h e i m a g e i s l o c a t e d o n t h e o p p o s i t e o f t h e l e n s a s t h e o b j e c t , w h i c h m a k e s i t a r e a l i m a g e . N o w t h a t w e k n o w b o t h t h e o b j e c t a n d i m a g e d i s t a n c e s , w e c a n u s e t h e d e f i n i t i o n o f l i n e a r m a g n i f i c a t i o n t o o b t a i n s i z e o f t h e i m a g e : n = 1 n = 1 . 3 2 9 1 2 θ 2 θ 1 θ 3 θ 2 n = 1 . 5 2 3 P h y s i c s 7 C S p r i n g 2 3 : B l o c k 1 5 E x e r c i s e s & Q / P s 2 3 3 2 M = h i h o = − i o ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ , h i = − i o ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ h o = − 5 . 2 5 c m 7 c m ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1 c m ( ) = − . 7 5 c m ....
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## This note was uploaded on 09/01/2009 for the course PHY 7C taught by Professor Mahmud during the Spring '08 term at UC Davis.

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7C%20S03%20Bk%2015%20Exercises%20and%20Q-Ps - P h y s i c s...

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