An object 0.400 cm tall is placed 18.5 cm to the left of the vertex of a convex

Question

An object 0.400 cm tall is placed 18.5 cm to the left of the vertex of a convex spherical mirror having a radius of curvature of 24.5 cm .

Part A

Calculate the position of the image. Express your answer in centimeters to two significant figures.

Part B

Calculate the size of the image. Express your answer in centimeters to three significant figures.

Part C

Find the orientation (upright or inverted) and the nature (real or virtual) of the image.

options:

Upright and real

upright and virtual

inverted and real

inverted and virtual

Explanation / Answer

A) 1/v +1/u = 2/r
v is image position , u is object position and r is radius of curvature of mirror.
for real object u is +ve, and r for convex mirror is -ve
1/v + 1/18.5 = -2/24.5
v = -7.39 cm
Hence image is vritual and 7.37 cm to right of mirror.

B) Magnification = -v/u = - ( -7.37/18.5) = 0.399
    +ve sign mean image is upight.
size of image = size of object* magnitude of magnfication = 0.4*0.399 = 0.159 cm

C) -ve sign of v , implies image is virtual
    +ve sign of magnification , implies it is upright.
hence option 2 is correct

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