4.5 ᴄᴍ ɴᴇᴇᴅʟᴇ ɪs ᴘʟᴀᴄᴇᴅ 12 ᴄᴍ ᴀᴡᴀʏ ғʀᴏᴍ ᴀ ᴄᴏɴᴠᴇx ᴍɪʀʀᴏʀ ᴏғ ғᴏᴄᴀʟ ʟᴇɴɢᴛʜ 15 ᴄᴍ. ɢɪᴠᴇ ᴛʜᴇ ʟᴏᴄᴀᴛɪᴏɴ ᴏғ ɪᴍᴀɢᴇ ᴀɴᴅ ᴍᴀɢɴɪғɪᴄᴀᴛɪᴏɴ. ᴅᴇsᴄʀɪʙᴇ ᴡʜᴀᴛ ʜᴀᴘᴘᴇɴs ᴛᴏ ᴛʜᴇ ɪᴍᴀɢᴇ ᴀs ᴛʜᴇ ɴᴇᴇᴅʟᴇ ɪs ᴍᴏᴠᴇᴅ ғᴀʀᴛʜᴇʀ ғʀᴏᴍ ᴛʜᴇ ᴍɪʀʀᴏʀ.
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Answer:
Given: Height of the needle, h
1
=4.5cm.
Object distance, u=−12cm.
The focal length of the convex mirror, f=15cm.
Image distance, v The value of v can be obtained using the mirror formula.
v
1
+
u
1
=
f
1
v
1
+
−12
1
=
15
1
v
1
=
12
1
+
15
1
v
1
=
60
9
∴v≈6.7cm
Hence, the image of the needle is 6.7 cm away from the mirror. Also, it is on the other side of the mirror.
The image size is given by the magnification formula.
m=
h
h
′
=−
u
v
h
′
=
12
6.7×4.5
⇒h
′
=+2.5cm
So, m=
4.5
2.5
m=0.56
The height of the image is 2.5cm. The positive sign indicates that the image is erect, virtual, and diminished. If the needle is moved farther from the mirror, the size of the image will reduce gradually.
hope it's helpful for you to learn
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