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Chapter 5: Q93P (page 1156)

A convex spherical mirror with a focal length of magnitude 24.0 cm is placed 20.0 cm to the left of a plane mirror. An object 0.250 cm tall is placed midway between the surface of the plane mirror and the vertex of the spherical mirror. The spherical mirror forms multiple images of the object. Where are the two images of the object formed by the spherical mirror that are closest to the spherical mirror, and how tall is each image?

Short Answer

Expert verified

The images are 7.06 cm and -13.3cm from the mirror.

The height of the images are 0.177cm and 0.111cm.

Step by step solution

01

Step 1:Relationship between object and image distance and height.

Object鈥檚 distance is s and image distance is s鈥�.

The relationship is 1s+1s'=1f

Object鈥檚 height is y and image height is y鈥�,

Therefore y'=-s'sy

02

Step 2:Calculation of the distance of images from the mirrors.

Image 1.

s=20cm2=10cm

Using the relationship of distance between object and mirror,

s'=sfs-f=10*-2410--24=-7.06cm

Image 2.

The focal length will be the same whereas the distance of the object will become 30cm.

Using the relationship of distance between object and mirror,

s'=sfs-f=30*-2430--24=-13.3cm

03

Calculation of the height of the image.

The height of the object is given as 0.25 cm.

Using the relationship between the height of image and object ,

Image 1.

y'=-s'sy=-(-7.0610)*0.25=0.177cm

Image 2.

y'=-s'sy=-(-13.330)*0.25=0.111cm

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