Questions: Mirror Image Formation and Ray Diagrams

Question 1

An object is placed 5 cm in front of a concave mirror with focal length 10 cm (inside the focal point). What type of image forms?

• A. A real, inverted image on the same side as the object
• B. A virtual, upright, magnified image located behind the mirror
• C. No image forms, because objects inside the focal length produce no reflection
• D. A real, upright image located behind the mirror

Answer: (B)

When an object is inside the focal length of a concave mirror (d_o < f), the reflected rays diverge and must be extended backward to find their apparent source. This yields a virtual image (d_i < 0) behind the mirror that is upright and magnified. This is exactly how a makeup mirror works — you sit inside the focal length to get a magnified, upright view. The common misconception is that concave mirrors always form real images; they only do so when the object is beyond the focal point.

Question 2

A convex mirror has a focal length of −20 cm. An object is placed 30 cm in front of it. What can be said with certainty about the image?

• A. The image is real, inverted, and located in front of the mirror
• B. The image is real, upright, and located behind the mirror
• C. The image is virtual, upright, and located behind the mirror
• D. The image location depends on where exactly the object is placed relative to the focal point

Answer: (C)

Convex mirrors have a negative focal length, which means their focal point is behind the mirror (virtual focus). Applying the mirror equation: 1/d_i = 1/f − 1/d_o = 1/(−20) − 1/30 = −5/60, so d_i = −12 cm. The negative value confirms the image is behind the mirror — virtual. Magnification m = −d_i/d_o = 12/30 > 0, so the image is upright and diminished. Convex mirrors ALWAYS produce virtual, upright, diminished images regardless of object position, which is why they are used for wide-angle surveillance.

Question 3

A convex mirror always produces a virtual, upright, diminished image regardless of where the object is placed.

• T. True
• F. False

Answer: True

This is true. Because a convex mirror has a negative focal length, the mirror equation always yields a negative d_i (image behind the mirror) and a positive magnification less than 1 for any positive object distance. The focal point is virtual (behind the mirror), so parallel rays never converge in front of it — no real image can form. This is the key difference from concave mirrors, which can produce either real or virtual images depending on object position.

Question 4

A negative magnification value (m < 0) from the mirror equation indicates that the image is smaller than the object.

• T. True
• F. False

Answer: False

The sign of magnification encodes orientation, not size. A negative magnification means the image is inverted (upside down) relative to the object. The absolute value |m| determines size: |m| > 1 means the image is enlarged, |m| < 1 means diminished, |m| = 1 means same size. For example, a concave mirror forming a real image far beyond the center of curvature gives m = −3, meaning the image is inverted AND three times larger than the object.

Question 5

Why does placing an object inside the focal length of a concave mirror produce a virtual image rather than a real image? What does this mean physically?

Model answer: When the object is inside the focal length, the reflected rays diverge after reflection — they never actually converge in front of the mirror. Instead, an observer sees rays appearing to come from a point behind the mirror. This apparent source is the virtual image: light does not actually pass through it, and it cannot be projected onto a screen. Mathematically, d_o < f makes 1/d_i negative (d_i < 0), confirming the image is behind the reflecting surface.

The key physical point is that 'image location' always means where rays converge or appear to diverge from. A real image occurs when reflected rays actually cross in space in front of the mirror — you could catch it on a screen. A virtual image occurs when reflected rays diverge; the eye traces them backward to an apparent source that has no actual light. The focal point is the dividing line: objects beyond f produce converging reflected rays (real image); objects inside f produce diverging reflected rays (virtual image).