Question

an electric lamp and screen are placed on the table in a line at a distance of 1 metre in that position of convex lens of focal length 21 will the image of lamp be sharp​

Answer 1

ANSWER

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.

You will get a quadratic relation between x,

f and d as x

2

- 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 x

1

=70cm and x

2

=30cm

solution

December 26, 2019

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Answer 2

★The distance between the lamp and screen is 100cm and 'x' be the distance between lamp and lens.

★From , we have u= -x and v=100-x , f= 21

★Substituting these in lens formula,

★We get

$\frac{1}{21} = \frac{1}{(100 - x)} + \frac{1}{x}$

★After solving this equation ,we get

${x}^{2} - 100x + 2100 = 0$

✈︎It is a quadratic equation . Hence we get two solution . The solution of the above equation are

${x}^{2} - 70x - 30x + 2100 = 0$

$x(x - 70) - 30(x - 70) = 0$

$(x - 70)(x - 30) = 0$

☘︎x=70cm and x= 30 cm.

$f$

★we can place the lens at a distance of 70cm or 30 cm from the bulb .we get sharp image.