Honeysuckle Creek – The story of Tom Reid, A little Dish and Neil Armstrong’s First Step - problem solved #2

This post solves a mathematic problem on Page 32 of the non-fiction book: “Honeysuckle Creek – The story of Tom Reid, A little Dish and Neil Armstrong’s First Step”, Andrew Tink, 2018

Problem: An object 2cm, high is held at a distance of 60cm from a convex lens of focal length of 20cm. Find the nature, position, and size of the image.

1. Given:

• Object height (h₁) = 2 cm
• Object distance (u) = -60 cm (negative sign convention)
• Focal length (f) = 20 cm

2. Find Image Distance (v):

• Use the lens formula: 1/f = 1/v - 1/u
• Substitute the given values: 1/20 = 1/v - 1/(-60)
• Simplify: 1/20 = 1/v + 1/60
• 1/v = 1/20 - 1/60
• 1/v = (3 - 1) / 60
• 1/v = 2/60
• v = 60/2
• v = 30 cm

3. Find Image Height (h₂):

• Use the magnification formula: h₂/h₁ = -v/u
• Substitute the values: h₂/2 = -30/(-60)
• h₂/2 = 1/2
• h₂ = 1 cm

4. Determine Nature of Image:

• Since the image distance (v) is positive, the image is real.
• The magnification (h₂/h₁) is positive and less than 1, so the image is inverted and diminished.

Therefore:

• The image is real, inverted, and diminished.
• The image is formed 30 cm from the lens on the opposite side of the object.
• The image height is 1 cm.

Shalom,

Ozhamada