Question

an auto vehicle has a convex mirror with radius of curvature 6 metre to see any other vehicle is at a distance of 6 metre from the mirror, then calculate the position and siof it's reflection in the mirror at that time​

Answer 1

Given :

In the convex mirror,

Radius of curvature = 6m

Object distance = - 6m

To find :

The position of the reflection in the mirror.

Solution :

» The focal length of a spherical mirror is equal to half of its radius of curvature so,

$\sf f = \dfrac{R}{2} = \dfrac{6}{2} = 3 \: m$

Now, using mirror formula that is,

» A formula which gives the relationship between image distance, object distance and focal length of a sperical mirror is known as the mirror formula .i.e.,

$\boxed{ \bf \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f} }$

where,

• v denotes Image distance
• u denotes object distance
• f denotes focal length

now, substituting all the given values,

$\leadsto{ \sf \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f} }$

$\leadsto{ \sf \dfrac{1}{v} + \dfrac{1}{( - 6)} = \dfrac{1}{3} }$

$\leadsto{ \sf \dfrac{1}{v} - \dfrac{1}{6} = \dfrac{1}{3} }$

$\leadsto{ \sf \dfrac{1}{v} = \dfrac{1}{3} + \dfrac{1}{6} }$

$\leadsto{ \sf \dfrac{1}{v} = \dfrac{2 + 1}{6} }$

$\leadsto{ \sf \dfrac{1}{v} = \dfrac{3}{6} }$

$\leadsto{ \sf \dfrac{1}{v} = \dfrac{1}{2}}$

$\leadsto \underline{ \boxed{ \sf v = 2 \: m}}$

thus, the position of the reflection in the mirror is 2m.