Questions: Spherical Mirror Formula and Sign Conventions

Question 1

An object is placed 10 cm in front of a concave mirror with focal length 15 cm (the object is inside the focal length). Using 1/f = 1/o + 1/i, what type of image does the mirror form?

• A. Real, inverted, and magnified — concave mirrors always form real images
• B. Virtual, upright, and magnified — the formula gives a negative image distance
• C. Virtual, inverted, and reduced — the object is too close to form a proper image
• D. No image forms — the formula is only valid when the object is beyond the focal point

Answer: (B)

Substituting: 1/15 = 1/10 + 1/i → 1/i = 1/15 − 1/10 = −1/30, so i = −30 cm. The negative image distance means the image is virtual (behind the mirror). Magnification m = −i/o = −(−30)/10 = +3, so the image is upright and 3× larger than the object. The misconception in option A — that concave mirrors always form real images — is only true when the object is beyond the focal point. Inside the focal point, a concave mirror acts like a magnifying glass, forming a virtual image.

Question 2

A car's convex rear-view mirror has a focal length of −25 cm. An object is 50 cm away. What does the negative image distance in the solution tell you?

• A. The image is real and forms in front of the mirror where you can project it on a screen
• B. The image is virtual and appears to be located behind the mirror's surface
• C. The calculation is invalid because convex mirrors cannot form images of real objects
• D. The object is on the wrong side of the mirror

Answer: (B)

For a convex mirror, f is negative. Solving: 1/(−25) = 1/50 + 1/i → 1/i = −1/25 − 1/50 = −3/50, so i ≈ −16.7 cm. The negative i means the image is behind the mirror — a virtual image that light rays never actually pass through. Your eye traces the diverging reflected rays backward and perceives the image as if it were behind the glass. This is the image you see in a rear-view mirror: always upright, always smaller, always virtual.

Question 3

A concave mirror with a positive focal length usually forms a real image, regardless of where the object is placed.

• T. True
• F. False

Answer: False

A concave mirror forms a real image only when the object is beyond the focal point (o > f). When the object is between the focal point and the mirror (o < f), the reflected rays diverge and the mirror forms a virtual, upright, magnified image — the same principle used in makeup mirrors and shaving mirrors. The mirror equation reflects this: when o < f, the formula gives a negative image distance, indicating a virtual image. 'Concave always means real' is one of the most common misconceptions in mirror optics.

Question 4

For a convex mirror, the focal length is negative because the focal point is located behind the mirror on the non-reflecting side.

• T. True
• F. False

Answer: True

The sign convention is grounded in the direction of light travel: positive distances are measured in the direction from which light arrives (in front of the mirror), and negative distances are measured behind it. A convex mirror's center of curvature and focal point both lie behind the reflecting surface — they are in the region where light does not actually travel after reflection. Therefore f is negative for a convex mirror. This is why convex mirrors can only form virtual images: with f negative, i is always negative regardless of object distance.

Question 5

Why does the sign convention for mirror equations define positive distances in the direction of incoming light rather than using some other arbitrary convention?

Model answer: The sign convention encodes the physics of image formation. Distances measured in the direction light travels after reflection correspond to real images — places where reflected rays actually converge. Distances in the opposite direction correspond to virtual images — apparent locations behind the mirror where diverging rays seem to originate. A consistent convention tied to light propagation direction means the sign of the image distance directly tells you whether the image is real (positive) or virtual (negative), without needing separate rules for each case.

This is why the sign convention is not arbitrary: it aligns the mathematics with the physical distinction between real and virtual images. Real images can be projected on a screen; virtual images cannot. The formula's sign outputs this answer automatically when the convention is applied correctly, making the mathematics directly interpretable as physics.