Answer :
Answer:
To find the position and nature of the image formed by a convex mirror, we can use the mirror formula:
1
=
1
+
1
f
1
=
v
1
+
u
1
where:
f is the focal length of the mirror (for a convex mirror, this is positive).
v is the image distance (we need to find this).
u is the object distance (this is negative in the mirror formula as it is measured opposite to the direction of the incident light).
Given:
=
+
15
f=+15 cm (convex mirror, so focal length is positive).
=
−
20
u=−20 cm (object distance is always taken as negative in mirror formula).
We need to find
v. Rearranging the mirror formula to solve for
v:
1
=
1
−
1
v
1
=
f
1
−
u
1
Substituting the given values:
1
=
1
15
−
1
−
20
v
1
=
15
1
−
−20
1
1
=
1
15
+
1
20
v
1
=
15
1
+
20
1
To add these fractions, we need a common denominator. The least common multiple of 15 and 20 is 60. Rewriting the fractions with a common denominator:
1
15
=
4
60
,
1
20
=
3
60
15
1
=
60
4
,
20
1
=
60
3
So,
1
=
4
60
+
3
60
=
7
60
v
1
=
60
4
+
60
3
=
60
7
Thus,
=
60
7
≈
8.57
cm
v=
7
60
≈8.57cm
The image distance
v is positive, indicating that the image is formed on the same side of the mirror as the object (a characteristic of virtual images formed by convex mirrors).
Nature of the Image:
Position: The image is located 8.57 cm behind the convex mirror.
Nature:
The image is virtual (as it is formed behind the mirror and cannot be projected onto a screen).
The image is erect (maintains the same orientation as the object).
The image is diminished (smaller than the object).
In summary, the image formed by the convex mirror is located 8.57 cm behind the mirror, virtual, erect, and diminished.
Explanation:
