A 4.5 cm needle placed 12cm away from convex mirror of focal length 15cm. Give the location of image and magnification. Describe what happens to the image as the needle is moved farther from the mirror.?

Question

Answer

Answer

Given :-

u = - 12 cm

f = + 15 cm

Solution :-

Using lens formula,

1/f = 1/u + 1/v

⇒ 1/v = 1/f - 1/u

⇒ 1/v = 1/15 - 1/- 12

⇒ 1/v = 60/9

⇒ v = 6.7 cm

Magnification, m = - (- v/u) = h₂/h₁

⇒ m = - 6.7/- 12

⇒ m = 0.558

m = h₂/h₁

h₂ = h₁ × m

⇒ h₂ = 0.558 × 4.5

⇒ h₂ = 2.5 cm.

As the needle is moved further from the mirror, image moves to the focus and the size of image goes on decreasing.

Answer

Given

Height of needle (object) = 4.5 cm

Distance of needle from mirror (object distance) = -12 cm (negative sign indicates that the object is placed in front of the mirror)

Focal length of convex mirror = 15 cm

Calculations

Using the mirror formula, we can find the location of the image formed by the convex mirror.

1/f = 1/v + 1/u

where,
f = focal length of mirror
v = distance of image from mirror (image distance)
u = distance of object from mirror (object distance)

Substituting the given values, we get:

1/15 = 1/v + 1/-12

Solving for v, we get:
v = -20 cm (negative sign indicates that the image is formed behind the mirror)

Answer

The location of the image formed by the convex mirror is -20 cm from the mirror.

The magnification of the image can be found using the formula:
m = -v/u

Substituting the values, we get:
m = -(-20)/(-12) = 5/3

Therefore, the magnification of the image is 5/3.

Explanation

As the needle is moved farther from the mirror, the image formed by the convex mirror becomes smaller and moves closer to the focal point of the mirror. This is because the object distance (u) increases, and hence the image distance (v) decreases. When the object distance becomes equal to the focal length of the mirror, the image distance becomes infinite, and the image is formed at infinity. This is called the 'focal point' of the mirror. As the object distance increases beyond the focal point, the image is formed on the same side of the mirror as the object, and it becomes virtual, erect, and magnified.

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