Question

Q. A square wire of side 3 cm is placed 25 cm away from a concave mirror of focal length 10 cm. What is the area enclosed by the image of the wire? The centre of the wire is on the axis of the with it's two sides normal to the axis.
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Answer 1

Given:-

• A square wire of side 3 cm is placed 25 cm away from a concave mirror of focal length 10 cm. The centre of the wire is on the axis of the with it's two sides normal to the axis.

To Find :-

• What is the area enclosed by the image of the wire?

Solution:-

According to the Question

Firstly we will calculate the image position of the object (wire) .

• Type of Mirror = Concave Mirror

As we know that ,

• Focal Length ,f = -10cm
• Object distance ,u = -25 cm
• Height of object ,ho = 3cm

by using mirror formula

• 1/f = 1/u + 1/v

substitute the given value we get

↠ 1/-10 = 1/-25 + 1/v

↠ -1/10 = -1/25 + 1/v

↠ -1/10 + 1/25 = 1/v

↠ -5+2/50 = 1/v

↠ -3/50 = 1/v

↠ v = -50/3 cm

Now, calculating the height of the image by using magnification formula

• m = hi/ho = -v/u

putting the value we get

↠ hi/3 = -(-50/3)/-25

↠ hi/3 = -(50/3) /25

↠ hi= 3 × -(50/3)/25

↠hi = -50/25

↠ hi = -2cm

Now, calculating the area enclosed by the image of the square wire

↠ Area = (-2m) × (-2m)

↠ Area = 4m²

• Hence, the area enclosed by the image of the square wire is 4m².

Answer 2

$\large \dag$ Solutions :-

• Here by seeing the question firstly we should need to calculate the image position of the object.
• After seeing the question we come to know the Type of Mirror is Concave mirror .
• Here in the question given some values

1. Focal length = f =-10cm.
2. u = -25cm
3. ho =3cm.

Here we know the mirror formula that is

• 1/f = 1/u + 1/v
• Now applying the values
• 1/-10 = 1/-25 +1/v
• -5+2/50 =1/v
• -3/50 = 1/v
• v = -50/3cm.

And then let's find the height but to find Th is we know the formulae that is

• m = hi/ho=-v/u
• hi/3=(-50/3)/-25
• hi = -50/25
• hi = -2cm.

Then ,

• Area = -2cm × -2cm
• Area = -4cm^2.

Therefore, the area enclosed by the image of the wire =4cm^2.

Thank you :-