When the object is placed at a distance of 60 cm from the diverging sp

1.	When the object is placed at a distance of 60 cm from the diverging spherical mirror, the magnification producedis 0.5. Where should the object be placed to get a magnification of 1/3 ?
Answer» Given that, Object distance (u) = -60cm MAGNIFICATION (m) = 0.5 Solution: As, here in the Question we are given that object is placed AROUND 60cm from the mirror. So, Firstly we will find the distance of the image i.e v By using the magnification formula. After Getting the distance of the object we can EASILY find the focal length of the image By using the mirror formula. Then, we will find Distance of image for magnification of 1/3. By using mirror Formuala we will get the Required distance of the object to be placed to get a magnification of 1/3. ━━━━━━━━━ Let's Find out.!! ➠ m = -v/u ➠ 0.5 = -v/60 ➠ v = 30cm Now, According to mirror formula we can find the focal length of the Image. ➠ 1/u + 1/v = 1/F ➠ 1/-60 +1/-30 = 1/f ➠ 1/-60 + 1/40 = 1/f ➠ f = 60cm Distance of the image ➠ m = -v/u ➠ 1/3 = -u/v ➠ v = -u/3 Using mirror formula, ➠ 1/u + 1/v = 1/f ➠ 1/u + 1/-u/3 = 1/60 ➠ 1/u - 3/4 = 1/60 ➠ -2/u = 160 ➠ u = -120 cm Hence, the object should be placed at 120 cm

When the object is placed at a distance of 60 cm from the diverging spherical mirror, the magnification producedis 0.5. Where should the object be placed to get a magnification of 1/3 ?

Answer»

Given that,

Object distance (u) = -60cm
MAGNIFICATION (m) = 0.5

Solution:

As, here in the Question we are given that object is placed AROUND 60cm from the mirror. So, Firstly we will find the distance of the image i.e v By using the magnification formula. After Getting the distance of the object we can EASILY find the focal length of the image By using the mirror formula. Then, we will find Distance of image for magnification of 1/3. By using mirror Formuala we will get the Required distance of the object to be placed to get a magnification of 1/3.

━━━━━━━━━

Let's Find out.!!

➠ m = -v/u

➠ 0.5 = -v/60

➠ v = 30cm

Now, According to mirror formula we can find the focal length of the Image.

➠ 1/u + 1/v = 1/F

➠ 1/-60 +1/-30 = 1/f

➠ 1/-60 + 1/40 = 1/f

➠ f = 60cm

Distance of the image

➠ m = -v/u

➠ 1/3 = -u/v

➠ v = -u/3

Using mirror formula,

➠ 1/u + 1/v = 1/f

➠ 1/u + 1/-u/3 = 1/60

➠ 1/u - 3/4 = 1/60

➠ -2/u = 160

➠ u = -120 cm

Hence, the object should be placed at 120 cm