The image (of a real object) formed by a concave mirror is twice the size of the object. The focal length of the mirror is 20 cm. The distance of the object from the mirror is (are) (B) 50 cm (C) 25 cm (D) 15 cm (A) 10 cm
The relationship between the object distance (denoted as "u"), the image distance (denoted as "v"), the focal length (denoted as "f"), and the magnification (denoted as "m") for a concave mirror is given by the mirror formula:
1/f = 1/v + 1/u
The magnification is defined as:
magnification (m) = -v/u
Given that the image formed by the concave mirror is twice the size of the object (m = -2), and the focal length is 20 cm, we can solve for the object distance using the magnification formula:
-2 = -v/u
v = 2u
Now, substitute the value of v into the mirror formula:
1/20 = 1/2u + 1/u
Combine the fractions on the right side:
1/20 = 3/2u
Solve for u:
u = (3/2) * 20
u = 30 cm
So, the distance of the object from the mirror is 30 cm. None of the given options (B) 50 cm, (C) 25 cm, (D) 15 cm, (A) 10 cm are correct.
Answers & Comments
Answer:
I think the answer is 50 cm.
[tex] - - - - [/tex]
The relationship between the object distance (denoted as "u"), the image distance (denoted as "v"), the focal length (denoted as "f"), and the magnification (denoted as "m") for a concave mirror is given by the mirror formula:
1/f = 1/v + 1/u
The magnification is defined as:
magnification (m) = -v/u
Given that the image formed by the concave mirror is twice the size of the object (m = -2), and the focal length is 20 cm, we can solve for the object distance using the magnification formula:
-2 = -v/u
v = 2u
Now, substitute the value of v into the mirror formula:
1/20 = 1/2u + 1/u
Combine the fractions on the right side:
1/20 = 3/2u
Solve for u:
u = (3/2) * 20
u = 30 cm
So, the distance of the object from the mirror is 30 cm. None of the given options (B) 50 cm, (C) 25 cm, (D) 15 cm, (A) 10 cm are correct.