Question

An object with a height of 4.31 cm is placed 12.6 cm from a concave mirror. Determine the radius of the mirror if the image appears 8.77 cm from the mirror. Also determine the image height. 4. Repeat question 6 but for a convex mirror.

Answer 1

Step-by-step explanation:

Given that,

Height of object = 4.31 cm

Distance of the object = -12.6 cm

Distance of the image = -8.77 cm

For concave mirror,

Using mirror's formula

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

`(1)/(f)=(1)/(-12.6)-(1)/(8.77)`

`(1)/(f)=-(10685)/(55251)`

`f=-(55251)/(10685)`

`f = -5.17\ cm`

Radius of the mirror is

`f = |(R)/(2)|`

`r=2f`

`r=2*5.17`

`r=10.34\ cm`

The magnification of the mirror,

`m=-(v)/(u)`

`(h_(i))/(h_(o))=(v)/(u)`

`h_(i)=-h_(o)*(v)/(u)`

`h_(i)=-4.31*(8.77)/(12.6)`

`h_(i)=-2.99\ cm`

Now, For convex mirror,

Using mirror's formula

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

`(1)/(f)=(1)/(-12.6)+(1)/(8.77)`

`(1)/(f)=(1915)/(55251)`

`f=(55251)/(1915)`

`f = 28.85\ cm`

Radius of the mirror is

`f = (R)/(2)`

`r=2f`

`r=2*28.85`

`r=57.7\ cm`

The magnification of the mirror,

`m=-(v)/(u)`

`(h_(i))/(h_(o))=(v)/(u)`

`h_(i)=-h_(o)*(v)/(u)`

`h_(i)=4.31*(8.77)/(12.6)`

`h_(i)=2.99\ cm`

Hence, This is the required solution.