Question

An electric lamp and a screen are placed on the table , in a line at a distance of 1m. In what positions of the convex lens of focal length be of f = 21cm will the image of the lamp be sharp ?


No Spam please....​

Answer 1

let 'd' be distance between the lamp and screen and 'x' be the distance between lamp and lens .

by substituting these in lens formula,

we get

1/f = 1 / ( d - x ) + 1 /x

after solving this equation, we get

x ^2 - d x + fd = 0

it is a quadratic equation. hence we get two solutions. the solutions of the above equations are

x = [ d + √(d^2 - 4 fd) ] / 2 .......(1)

given that f =21 cm and d =1 m = 100cm.

substituting these values in equation 1,

we get

$x1 = 70cm \: and \: x2 = 30cm.$

NOTE ; image of the lamp can be sharp only when f is less than or equal to 25CM.

I hope it helps you Akka....

Answer 2

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The following steps are to be taken to solve the query:

1) Using the distances in the diagram above we get u=−x and v=d−x.

2) Now, apply the lens formula and find the relation between the distances.

$\dfrac{1}{f}$=$\dfrac{1}{x}$+$\dfrac{1}{d-x}$

You will get a quadratic relation between x,

f and d as x² - xd + fd = 0 -------(1)

3) Substitute the value of d=100 cm

and f=21 cm to find the value of x.

so when we put f=21 and d=100

finally

Substituting these values in equation 1,

we get x1 =70 cm and x2 =30 cm