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A convex lens, of focal length 20 cm, ha...

A convex lens, of focal length 20 cm, has a point object placed on its principal axis at distance of 40 cm from it. A plane mirror is placed 30 cm behind the convex lens. Locate the position of image formed by this combination

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We first consider the effect of the lens. For the lens, we have u=-40 cm and f= + 20 cm
Using the lens formula, we get
` (1)/(v_1) - (1)/(-40) = 1/20 " " therefore v_1 = + 40cm`
Had there been the lens only the image would have have been formed at `Q_1` . The plane mirror M is at a distance of 30 cm from the lens L. We can,therefore, think of `Q_1` as a virtual object, located at a distance of 10 cm, behind the plane mirror M. The plane mirror therefore forms a real image (of this virtual object `Q_1`) at Q, 10 cm in front of it.
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