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Question: An object is placed 50cm in front of a concave mirror of 60 cm radius. Determine the (a) focal length, (b) image distance, (c) linear magnification, (d) object size if the image produced was 3cm (e) define the image produced.

Answers and detailed explanation below

Step-by-step explanation

Object distance (u) = 50cm

Radius (r) = 60cm

Question a

Relationship between focal length and radius of curvature is given as

f = r/2

f = 60/2 = 30cm

Focal length is 30cm.

Question b

To get the image distance, we make use of the mirror formulae.

1/u + 1/v = 1/f

1/50 + 1/v = 1/30

1/v = 1/30 - 1/50

1/v = 50 - 30/150

1/v = 20/150

1/v = 2/15

2v = 15, v = 15/2 = 7.5cm

Image distance is 7.5cm

Question C

Linear magnification formulae is given as

M = -v/u

M = - 7.5/50

M = -0.15

The negative sign tells the type of image formed.

Question D

Ho is the object size, Hi is the object's size which is 3cm.

M = Hi/Ho

In this case we use the positive value of magnification since size can not be negative.

M = 0.15

0.15 = 3/Ho

3 = 0.15 × Ho

Ho = 3/0.15

Ho = 20cm.

Size of object is 20cm.

Question E

Since magnification is lesser than one, it implies that the image is diminished.

Since magnification is negative, it implies that the image is real.

Real images are always inverted and cannot be formed on a screen.