The image of an object placed at a distance of 30 cm on the principal axis of a concave mirror from its pole, is formed on the object itself.
Find :
(a) the focal length and
(b) linear magnification of mirror.
Answers
a) The focal length of the given concave mirror is 15 cm.
b) The linear magnification of the mirror is -1 .
a) Given,
• Distance of object from the pole of the concave mirror (u) = 30 cm
• Image is formed on the object itself.
=> Distance of image from the pole (v) of the mirror = 30 cm
• In a concave mirror, image is formed on the object when the object is placed at the centre of curvature (2F) of the mirror.
• Therefore, 2F = 30 cm
or, F (focal length) = 30 cm / 2
or, F = 15 cm
b) • Linear Magnification of a concave mirror is given by the formula :
m = - (v/u)
where m is the linear magnification,
v is the distance of the image from the mirror,
u is the distance of the object from the mirror,
and '-' sign means the image formed is inverted.
• Therefore, m = - (30 cm / 30 cm) = -1
• The image formed is inverted, and is of the same size as that of the object.
Answer:
a) The focal length of the given concave mirror is 15 cm.
b) The linear magnification of the mirror is -1 .
Explanation:
a) Given,
• Distance of object from the pole of the concave mirror (u) = 30 cm
• Image is formed on the object itself.
=> Distance of image from the pole (v) of the mirror = 30 cm
• In a concave mirror, image is formed on the object when the object is placed at the centre of curvature (2F) of the mirror.
• Therefore, 2F = 30 cm
or, F (focal length) = 30 cm / 2
or, F = 15 cm
b) • Linear Magnification of a concave mirror is given by the formula :
m = - (v/u)
where m is the linear magnification,
v is the distance of the image from the mirror,
u is the distance of the object from the mirror,
and '-' sign means the image formed is inverted.
• Therefore, m = - (30 cm / 30 cm) = -1
• The image formed is inverted, and is of the same size as that of the object.