A student holds a concave lens of focal length 20 cm, 30 cm from a candle…

Step 1. The image. $\dfrac{1}{v} = -\dfrac{1}{20\ \text{cm}} - \dfrac{1}{30\ \text{cm}} = -\dfrac{3 + 2}{60\ \text{cm}} = -\dfrac{1}{12\ \text{cm}}$, so $v = -12\ \text{cm}$.

Step 2. The size. $m = \dfrac{-12\ \text{cm}}{-30\ \text{cm}} = +0.4$.

Step 3. Why no screen. The rays spread out after the lens and never meet. Only the eye, tracing them back, sees an image.