help with part b im on last try MasteringPhysics: Homework a12 Google Chrome Sec

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help with part b im on last try

MasteringPhysics: Homework a12 Google Chrome Secure l https://session.masteringphysics.com/myct/itemView?assignmentProblemID 73835872 PHY 2049 801 Spring 2017 Homework #12 Exercise 34.10 Exercise 34.10 Part A Where is the image of your 5.0-cm-tall nose located? Follow the sign rules. You hold a spherical salad bowM 68 cm in front of your face with the bottom of the bowi facing you. The salad bovM is made of Express your answer to two significant figures and include the appropriate urlits polished metal with a 20-cm radius of curvature. s' 8.7 cm Submit My Answers Give Up Correct Part B What is the image's size? Express your answer to two significant figures and include the appropriate units. 0.73 cm My Answers Give Up Submit Incorrect: One attempt remaining: Try Again Part C

Explanation / Answer

We know that the shape of the spherical salad bowl is like convex spherical mirror so for any convex spherical mirror the image of your nose is virtual, upright and reduced

Part A:

From the spherical mirror equation we can write as

(1/f) = (1/d) + (1/i )

i = ( f d ) / [ d - f ]

here f = focal length of the spherical mirror = - R/2 = - (20 cm )/2 = -10 cm

{ R =Radius of curvature , For convex mirror the focal length is negative }

d = Object distance from the mirror = Distance between person's face and mirror = 68 cm

i = Image distance

On substituting we get

i = [ (-10 cm ) (68 cm ) ] / [ (68 cm - (-10 cm )]

i = - 8.72 cm

{ -ve sign indicates the image is virtual and it is located 8.72 cm behind the spherical mirror }

Part B:

We can find the image size using magnification formula i.e

m = - i / d = y' / y

here y' is image height and y = object height = 5.0 cm

- (-8.72 cm ) / (68 cm ) = ( y' ) / ( 5.0 cm )

y' = 0.641 cm

Therefore the height of the image is 0.641 cm .

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