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A 10 mm Long Awl Pin is Placed Vertically in Front of a Concave Mirror. A 5 mm Long Image of the Awl Pin is Formed at 30 Cm in Front of the Mirror. The Focal Length of This Mirror is?
By BYJU'S Exam Prep
Updated on: September 25th, 2023
(a) 30 cm
(b) 20 cm
(c) 40 cm
(d) 60 cm
A 10 mm long awl pin is placed vertically in front of a concave mirror. A 5 mm long image of the awl pin is formed at 30 cm in front of the mirror. The focal length of this mirror is 20 cm.
Step 1: Given data
Since the image is real and is formed in front of the mirror,
v = -30 cm
Height of the image hi = 5 mm = 0.5 cm
Height of the object h0 = 10 mm = 1 cm
Step 2: Now we have to calculate the Image Distance
Since the magnification for a concave mirror is specified as,
m = hi/h0 = -v/u
substituting the values in above equation, we get,
0.5/1 = – (-30)/u
On rearranging we get
u = 30/0.5 = 60
Since, the object is in front of the mirror,
u = -60 cm
Step 3: Now we have to Calculate the Focal Length
According to the mirror formula, the focal length is given by
1/f = 1/v + 1/u
Now substituting the values in above equation we get,
1/f = 1/-30 + 1/-60
= -(2 + 1)/ 60
On simplifying we get
= -3/60
= -1/20
f = -20 cm
Focal length cannot be negative so f = 20cm
Summary:-
A 10 mm Long Awl Pin is Placed Vertically in Front of a Concave Mirror. A 5 mm Long Image of the Awl Pin is Formed at 30 Cm in Front of the Mirror. The Focal Length of This Mirror is?
In front of a concave mirror, a vertically positioned 10 mm long awl pin is positioned. At 30 cm in front of the mirror, a 5 mm long picture of the awl pin is created. This mirror’s focal length is 20 cm.
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