Question

An object is placed at distance 8 cm and the front of convex lens of focal length 20cm the image formed is​

Answer 1

Given:

• Object distance = - 8 cm

Object distance is always negative as distance is measured from the optical centre of the lens

• Focal length = + 20 cm

Focal length of a convex mirror is positive

_____________

To find :

• Image distance

_____________

Solution :

As per the lens formula ,

$\bigstar\boxed{\mathtt{\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u} }}$

here ,

• f = focal length
• v = image distance
• u = object distance

Now on substituting the given values in the above equation we get ,

$\implies\mathtt{\dfrac{1}{20} = \dfrac{1}{v} - \dfrac{1}{ - 8} }$

$\implies\mathtt{\dfrac{1}{20} = \dfrac{1}{v} + \dfrac{1}{ 8} }$

$\implies\mathtt{ \dfrac{1}{v} = \dfrac{1}{20} - \dfrac{1}{ 8}}$

$\implies\mathtt{ \dfrac{1}{v} = \dfrac{2 - 5}{40} }$

$\implies\mathtt{ \dfrac{1}{v} = \dfrac{ - 3}{40} }$

$\implies\mathtt{v = \dfrac{ - 40}{3} }$

$\implies\mathtt{ \red{v = - 13.33 \: cm }}$

The image is formed at a distance of 13 .33 cm on the same side as that of the object

_______________

Additional formulas :-

Lens :-

• Magnification

$\implies \mathtt{m = \dfrac{v}{u} = \dfrac{hi}{ho} }$

Mirror :-

• Mirror formula

$\implies\mathtt{\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u} }$

• Magnification

$\implies \mathtt{m = - \dfrac{v}{u} = \dfrac{hi}{ho} }$

Answer 2

Concept:

The Convex Lens equation states that 1/f = 1/v + 1/u is the lens formula. It connects a lens's focal length to the separation between an object in front of it and the image it creates.

Given:

Object distance, u = - 8cm

Focal length, f = 20cm

Find:

We need to determine the image distance, v.

Solution:

The object distance of a convex lens is negative because the distance when calculated from the optical centre of the lens is always negative.

The focal length of a convex mirror remains positive therefore, f = + 20cm while u = - 8cm

Where f is the focal length, v is the image distance, and u is the object distance, the formula is 1/f = 1/v + 1/u.

Therefore, the equation of lens formula becomes-

1/20 = 1/v + 1/-8

1/20 + 1/8 = 1/v

Therefore, 1/v = 2 + 5 / 40

1/v = 7/40

v =  40/7 cm

v = 5.71 cm

Thus, the distance of the image is 5.71 cm.

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