Question

What will be the height of image when an object 2mm is placed on the axis of a convex mirror at a distance of 20cm of radius of curvature 40cm ​

Answer 1

Question : -

What will be the height of an image when an object of height 2 mm is placed on the axis of a convex mirror at a distance of 20 cm of radius of curvature 40 cm ?

ANSWER

Given : -

When an object of height 2 mm is placed on the axis of a convex mirror at a distance of 20 cm of radius of curvature 40 cm.

Required to find : -

• Height of an image ?

Formula used : -

Mirror formula

(1)/(u) + (1)/(v) = (1)/(f)

Here,

• (1)/(u) = Distance of the object from the mirror
• (1)/(v) = Distance of the image from the mirror
• (1)/(f) = Focal length of the mirror

Solution : -

When an object of height 2 mm is placed on the axis of a convex mirror at a distance of 20 cm of radius of curvature 40 cm.

From this data we can conclude that;

• Distance of the object from the mirror (u) = -20 cm

Here,

Distance is negative since, the distance between the object and mirror is measured with respective mirror .

• Height of the image (ho) = 2 mm
• Radius of curvature of the convex mirror (r) = 40 cm

Since,

We know that;

Radius of curvature = 2 times the focal length

i.e.

r = 2f

This implies;

Focal length of the convex mirror = (r)/(2) = (40)/(2) = 20 cm

Hence,

• Focal length of the convex mirror (f) = 20 cm

Now,

Let's find the image distance (v)

Using the formula;

(1)/(u) + (1)/(v) = (1)/(f)

(1)/(-20) + (1)/(v) = (1)/(20)

The focal length of a convex mirror is positive (+ve)

(1)/(v) = (1)/(20) - (-1)/(20)

(1)/(v) = (1)/(20) + (1)/(20)

(1)/(v) = (1+1)/(20)

(1)/(v) = (2)/(20)

(1)/(v) = (1)/(10)

• v = 10 cm

Hence,

• The distance of the image from the mirror is 10 cm

Now,

Let's find the height of the image !

We know that;

Magnification (m) = (height of the image )/(height of the object)

However,

• (height of the image)/(height of the object) = (-v)/(u)

Using this let's find the height of the image.

(hi)/(ho) = (-v)/(u)

(hi)/(2) = (-[10])/(-20)

(hi)/(2) = (-10)/(-20)

(hi)/(2) = (1)/(2)

hi = (1)/(2) ÷ (1)/(2)

hi = (1)/(2) x (2)/(1)

hi = (2)/(2)

hi = 1mm

Therefore,

• Height of the image (hi) = 1mm

Answer 2

Answer:

The Height of The Image Formed By The Convex Mirror is 0.1cm Or 1mm

Explanation:

PLEASE REFER TO THE ATTACHMENT...