Question

An object of size 7.5cm is placed in front of a convex mirror of radius of curvature 25cm at a distance of 40cm. The size of the image should be


(1) 2.3 cm
(3) 1 cm
(2) 1.78 cm
(4) 0.8 cm​

Answer 1

♣GIVEN♣

• f= 25/2 cm

• u= -40 cm

♣TO FIND♣

• The size of the image.

♣SOLUTION♣

➤ Mirror formula,

• 1/v +1/u =1/f

→ 1/v= 2/25 - (1/(-40))

→ 1v = 2/25+ 1/40 = 21/200

→ v = 200/21 cm

➤ Now,

• Magnification = h'/h = -(v/u)

→ h'/7.5= -(200/(21×(-40))

→ h' =25/17

→ h' =1.47 cm

So the image is virtual and diminished.

Answer 2

$\huge{ \bold{ \fbox{ required \: answer}}}$

$\bold{ \underline{ \underline{answer}}}→$

(2) 1.78cm

$\bold{ \underline{ \underline{solution}}}→$

given :-

• size of object, h1 = +7.5cm
• radius of curvature, C = +25cm ( convex mirror)
• object distance, u = -40cm

we know that,

focal length,f = C/2

→ f = 25/2cm

_______________________

putting these values in the mirror formula:

1/f = 1/v + 1/u

→ 2/25 = 1/v - 1/40

→ 1/v = 2/25 + 1/40

→ 1/v = (16+5)/200

→ 1/v = 21/200

→ v = + 200/21 cm (in front of mirror)

_______________________

to find the size of image, we will calculate the magnification first,

now, magnification, m = -v/u

→ m = -(200/21)/-40

→ m = (200×1)/(21×40)

→ m = 5/21 cm

_______________________

we also have another formula for magnification, which is;

m = size of image,h2 / size of object, h1

→ 5/21 = h2 / 7.5

→ h2 = (5×7.5)/21

→ h2 = 37.5/21

→ h2 = 1.78 (approximately)

so, option c). 1.78 cm is correct

________________________

￣￣￣￣￣￣￣￣￣￣￣

$\bold{ \underline{ \underline{for more information}}}→$

✧ if the magnification has a plus sign, then the image is virtual and erect.

✧ if the magnification has a minus sign z then the image is real and inverted.

✧ if the magnitude of magnification is equal to 1, then the size of image is equal to size of object.

✧ if the magnitude of magnification is less than 1, then size of image is greater than size of object.

✧ if the magnitude of magnification is less than 1, then size of image is smaller than size of object