Question

in a certain pinhole camera, the screen is 10 cm from the pinhole. When the pinhole is placed 6 cm away from a tree ,a sharp imageof a tree 16 cm high if formed on the screen. Find height of the tree​

Answer 1

Height of the tree is 9.6 cm

Step-by-step explanation:

We know that, Magnification of an image is written as follows.

`\left((H_(i))/(H_(o))\right)=\left((D_(i))/(D_(o))\right)`

Where,

`\begin{array}{l}{\mathrm{H}_(0)=\text { height of the object }} \\ {\mathrm{H}_{\mathrm{i}}=\text { height of the image }} \\ {\mathrm{D}_(0)=\text { distance of the object }} \\ {\mathrm{D}_{\mathrm{i}}=\text { distance of the image }}\end{array}`

As per given question,

`\begin{array}{l}{\mathrm{H}_(1)=\text { height of the image }=\text { height of the image of the tree on screen }=16 \mathrm{cm}} \\ {\mathrm{D}_(0)=\text { distance of the object }=\text { distance of the tree from the pinhole }=6 \mathrm{cm}} \\ {D_(1)=\text { distance of the image }=\text { distance of the image from the pinhole }=10 \mathrm{cm}} \\ {\mathrm{H}_(0)=\text { height of the object }=\text { height of the tree }}\end{array}`

Substitute the values in the above formula,

`\begin{array}{l}{\left((H_(i))/(H_(o))\right)=\left((D_(i))/(D_(o))\right)} \\ {\left((16)/(H_(o))\right)=\left((10)/(6)\right)} \\ {\mathrm{H}_{\mathrm{o}}=\left((16 * 6)/(10)\right)} \\ {\mathrm{H}_{\mathrm{o}}=9.6 \mathrm{cm}}\end{array}`

Height of the tree is 9.6 cm.