Correct option is D
The correct answer is (d) −37.5 cm
Explanation:
• We use the mirror formula:
1/f = 1/v + 1/u,
where f is the focal length, v is the image distance, and u is the object distance.
• According to the sign convention for mirrors, in the case of a concave mirror, the object distance (u) is always negative and the focal length (f) is also negative.
• Given values:
u = −15 cm and f = −25 cm.
• Substituting these values in the mirror formula:
1/−25 = 1/v + 1/−15.
• Rearranging to solve for v:
1/v = 1/15 − 1/25.
• Taking LCM of 15 and 25 (which is 75):
1/v = (5 − 3) / 75
1/v = 2 / 75.
• Therefore,
v = −75 / 2 = −37.5 cm.
• The negative sign shows that the image is formed on the same side of the mirror as the object, indicating a real image.
Information Booster:
• For a concave mirror, when the object is placed between the focus (F) and the pole (P), the image formed is virtual, erect, and magnified.
• Linear magnification (m) is given by:
m = −v / u.
• In this case:
m = −(−37.5) / (−15) = −2.5.
• This means the image is real, inverted, and 2.5 times larger than the object.
