Apparent angular size with magnification: An angle measures 2.5°. When viewed through a glass that magnifies linear dimensions 3 times, what is the apparent angular size?

Introduction / Context:Magnification enlarges linear dimensions in the image. For small angles (and in standard optical approximations), the apparent angular size scales in direct proportion to linear magnification.

Given Data / Assumptions:

• True angle = 2.5°.
• Magnification M = 3 (linear).
• Small-angle/paraxial approximation so apparent angle scales with M.

Concept / Approach:Apparent angular size θ′ ≈ M * θ when an object is viewed through a magnifier producing linear magnification M, provided angles are modest and the setup is in the usual near-axis geometry.

Step-by-Step Solution:θ = 2.5°M = 3θ′ = M * θ = 3 * 2.5° = 7.5°

Verification / Alternative check:As a sanity check, doubling the magnification would double the angle; tripling should triple. 7.5° is exactly triple 2.5°.

Why Other Options Are Wrong:5°, 6°, 10° do not equal 3 * 2.5°. 2.5° ignores magnification entirely.

Common Pitfalls:Mistaking magnification as affecting only linear size but not apparent angle; for visual perception under paraxial conditions, apparent angle scales like linear magnification.

Final Answer:7.5°