Chapter 17, Problem 94A

To determine

Image position after flipping the spoon.

Answer to Problem 94A

  $v=1.8\text{cm}$ that is the image formed 1.8 cm behind the spoon.

Explanation of Solution

Given:

For the spoon part that holds the food,

Object position is in front of mirror, $u=-3\text{cm}$

Image position is behind the mirror, $v=9\text{cm}$

Formula Used:

The mirror formula is given as,

  $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

Here, $f$ is focal length of spherical mirror, $v$ is image position and $u$ is object position.

Calculation:

On substituting the values in mirror formula,

  $\begin{array}{l}\frac{1}{f}=\frac{1}{-3}+\frac{1}{9}\\ \Rightarrow f=\frac{-27}{6}=-4.5\text{cm}\end{array}$

So the focus of the concave part is $f=-4.5\text{cm}$

Now, on flipping the spoon the focus of the convex part will be $f=4.5\text{cm}$

Again putting the values $u=-3\text{cm}$ and $f=4.5\text{cm}$ in lens formula for convex part

  $\begin{array}{l}\frac{1}{4.5}=\frac{1}{-3}+\frac{1}{v}\\ \Rightarrow \frac{1}{v}=\frac{1}{4.5}+\frac{1}{3}\\ \Rightarrow v=\frac{4.5\times 3}{4.5+3}=1.8\text{cm}\end{array}$

As, $v=1.8\text{cm}$ it means the image formed is virtual.

Conclusion:

Therefore, the image formed is 1.8 cm behind the spoon.