Chapter 23, Problem 79GP

To determine

Part (a) To Determine:

The type of mirror to be used.

Answer to Problem 79GP

Solution:

convex mirror

Explanation of Solution

Since we know that image formed is virtual and upright and smaller than the real object. We know that image formed by convex mirror are virtual and erect and magnification of convex mirror is always positive. Here in this case also image is virtual and erect, and magnification is positive because image is upright.

To determine

Part (b) To Determine:

The location of image

Answer to Problem 79GP

Solution:

24.9 cm

Explanation of Solution

Given:

Given that distance of object from mirror (say)$u=32\text{cm}$

Height of object (say)$h_1=4\cdot 5\text{cm}$

Height of image (say)$h_2=3\cdot 5\text{cm}$, and image is virtual and upright

Formula used:

$\begin{array}{l}\text{magnification of mirror}\\ =sizeofimage\left(h_2\right)/sizeofobject\left(h_1\right)\\ =v/-u\end{array}$

Calculation:

$\begin{array}{l}\text{magnification of mirror= size of image }\left({\text{h}}_{\text{2}}\right)\text{/size of object }\left({\text{h}}_{\text{1}}\right)\hfill \\ m=3\cdot 5cm/4\cdot 5cm=7/9\hfill \\ \therefore m=v/-u,so\left(v/-u\right)=7/9\hfill \\ \begin{array}{l} v=\left(-u\right)\times 7/9\\ =-\left(-32\right)\times 7/9\\ =224/9\text{ cm }\\ =24.9\text{ cm}\end{array}\hfill \end{array}$

To determine

Part (c) To Determine:

We must find the focal length of the mirror.

Answer to Problem 79GP

Solution:

112 cm

Explanation of Solution

Given:

Given that distance of object from mirror (say)u= 32 cm

Height of object (say)h₁ = 4∙5 cm

Height of image (say)h₂ = 3∙5 cm, and image is virtual and upright

Formula used:

Mirror formula for focal length $1/f=1/v+1/u$

Calculation:

since we have got the value of $v=\text{224/9 cm}$

now mirror formula for focal length

$\begin{array}{l}1/f=1/v+1/u\hfill \\ 1/f=1/\left(224/9\right)+1/\left(-32\right)\hfill \\ 1/f=9/224–1/32=\left(9-7\right)/224=2/224=1/112cm\hfill \\ f=112\text{ cm}\hfill \end{array}$

To determine

Part (d) To Determine:

We must find the radius of curvature of the mirror.

Answer to Problem 79GP

Solution:

224 cm

Explanation of Solution

we will find the radius of curvature of mirror by formula $2/R=1/f$ 2/R = 1/f

Given:

Given that distance of object from mirror (say)u= 32cm

Height of object (say)h₁ = 4∙5 cm

Height of image (say)h₂ = 3∙5 cm, and image is virtual and upright

Formula used:

Radius of curvature formula $2/R=1/f$

Calculation:

Since we know radius of curvature R is related to focal length f by

$2/R=1/f$ and we have found the value of $f=112\text{cm}$

So $R=2f=2\times 112\text{cm = 224 cm}$