Question

One concave mirror in cut at middle and then separated as in figure. Find the separation between the images

Ans is 30mm show working pls

Answer 1

The separation between the images is 6 mm

Explanation:

The magnification is given by the formula:

m = hi/ho

hi = Height of image

ho = Height of object

Now,

hi/ho = -v/u

Where,

v = Image distance

u = Object distance

Now, on using mirror formula, we get,

-v/u = f/(f - u)

Where,

f = Focal length = - 20 cm

u = Object distance = - 30 cm

⇒ hi/ho = f/(f - u)

On substituting the values, we get,

hi/ho = -20/(-20 - (-30))

hi/ho = -20/(-20 + 30) = -20/10 = - 2 cm

hi/-5 mm = -2 cm

∴ hi = -2 × 10⁻² × -5 × 10⁻³ = 10⁻⁴ m

Now,

v = -(hi/ho) × u

On substituting the values, we get,

v = -(10⁻⁴/(5 × 10⁻³)) × - 30 × 10⁻²

∴ v = 0.006 m = 6 mm