Question

A Concave lens has focal lenght of 20cm. At what distance from the lens a 5cm tall object object be placed so that it forms an image at 15cm from the lens? Also Calculate the size of image and define its nature.​

Answer 1

Given that,

• Image distance =(v) = -15 cm  [ Negative due to concave lens  ]

• Focal length = (f) = -20cm [ Negative due to concave lens ]

• Let image distance be u.

we know the lens formula,

⇒ 1/v-1/u = 1/f

⇒ 1/-15 cm-1/u = 1/-20cm

⇒ 1/u = 1/20 cm-1/-15 cm [ taking LCM and solving it we get the follow ]

⇒ 1/u = 3-4/60 cm

⇒ 1/u = -1/60cm

⇒ - u = 60 cm

⇒ u = -60 cm

Therefore, the object is placed 60 cm away from the concave lens on the same as image.

Then,

• Height of the image (h1) = 5 cm

• Height of the image (h2) = ?

• We know the magnification formula,

• Magnification be m say

⇒ M = h2/h1 = v/u

• Substitute v & u value in the equation we get,

⇒ m = h2/5cm = -15cm/-60cm

⇒ m = h2/5cm = 1/4 cm

⇒ m = 4×h2 = 5×1

⇒ m = h2 = 5cm/4

⇒ m = h2 = +1.25 cm.

Therefore, the height of the image is +1.25cm [ positive sign shows that the image is virtual and erect ]

Hope this helps you.

Thank you for your question it had helped me to think.

Mark me as brainiest it took lot of time for me to type.