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Chapter 5: Q67P (page 1154)

Question:A concave mirror is to form an image of the filament of a headlight lamp on a screen 8.00mfrom the mirror. The filament is 6.00 mmtall, and the image is to be 24.0cmtall. (a) How far in front of the vertex of the mirror should the filament be placed? (b) What should be the radius of curvature of the mirror?

Short Answer

Expert verified
  1. The filament must be placed 20cm in front of the vertex of the mirror.
  2. The radius of the curvature of the mirror should be 41cm.

Step by step solution

01

Determine the position of the filament in front of the vertex of the mirror

a. Use the lateral magnification for a spherical mirror

Substitute the given values in the equation

Therefore, the filament must be placed 20cm in front of the vertex of the mirror.

02

Determine the radius of the curvature of the mirror

b. Use the object-image relationship

Substitute the given values

Therefore, the radius of curvature of the mirror is 41.cm.

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