Question

8. A 5 cm tall object is placed perpendicular to the principal axis of a convex lens
of focal length 20 cm. The distance of the object from the lens is 10 cm. Find the
size of the image formed, using the lens formula.​

Answer 1

Answer:

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Explanation:

The size of the image is 10 cm and the image is real and inverted

Given that,

Height of object h = 5 cm

Focal length f = 20 cm

The distance of the object u = -30 cm

Using lens's formula

\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}

f

1

=

v

1

−

u

1

\dfrac{1}{20}=\dfrac{1}{v}-\dfrac{1}{-30}

20

1

=

v

1

−

−30

1

\dfrac{1}{v}=\dfrac{1}{60}

v

1

=

60

1

v = 60v=60

The image is formed at 60 cm on the other side from the lens.

The magnification is

m = \dfrac{v}{u}m=

u

v

m = \dfrac{60}{-30}m=

−30

60

m = -2m=−2

The image is real, inverted .

Size of the image,

m = \dfrac{h'}{h}m=

h

h

′

-2 = \dfrac{h'}{5}−2=

5

h

′

h' = -10 cmh

′

=−10cm

Hence, The size of the image is 10 cm and the image is real and inverted.

Answer 2

Question:

• A 5 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20 cm. The distance of the object from the lens is 10 cm. Find thesize of the image formed, using the lens formula.

☞Solution:

➝Let us assume something:

• Object distance→ u
• Image distance→ v
• Focal length→ f
• Size of the image→h'
• Size of the object→h

➝We have to find:

1. ➝Size of image(h')

➝From the above question, we get:

• u= -10cm ('-' sign as it is convex lens)
• f= 20cm
• h'=5cm

━☞Formula of lens is given by:

$= > \frac{1 }{f} = \frac{1}{v} - \frac{1}{u}$

➝Putting the values, we get:

$= > \frac{1}{15} = \frac{1}{v} - \frac{1}{( - 10)}$

$= > \frac{1}{15} = \frac{1}{v} + \frac{1}{10}$

$= > \frac{1}{v} = \frac{1}{15} - \frac{1}{10}$

$= > \frac{1 }{v } = \frac{2 - 3}{60}$

$= > \frac{1}{v} = \frac { - 1}{30}$

$= > v = - 30cm$

➝Hence, v(image distance)=-30cm

➜To find size of the image formed, we have:

$= > \frac{h'}{h} = \frac{v}{u}$

$= > h' = 15cm$

╭☞Hence size of the image is 15cm

✧Hope it helps you✧