An object 3.00m high is placed at a distance of 7.50m from a pin-hole camera. If the image height is 6.00 cm…

Analyze the question: A pin-hole camera forms an inverted image on the film. The object and image are on opposite sides of the pin-hole, and the two triangles formed are similar. So the magnification relation applies:

h_i / h_o = v / u

where

• h_i = image height
• h_o = object height
• v = distance from pin-hole to film
• u = distance from object to pin-hole

Given:

• h_o = 3.00 m = 300 cm
• u = 7.50 m = 750 cm
• h_i = 6.00 cm

Solution:

v = u × (h_i / h_o)

v = 750 cm × (6.00 / 300)

v = 750 × 0.02

v = 15.00 cm

(Check in metres: v = 7.50 × (0.06 / 3.00) = 7.50 × 0.02 = 0.15 m = 15 cm ✔)

Answer: The film is 15.00 cm from the pin-hole, which is option C.

Tip: In pin-hole camera questions, always convert everything to the same unit first. The mistake most students make is mixing metres and centimetres, which leads to wrong options like 150 cm or 1.5 cm. Remember: image/object = image distance/object distance.