A thin lens is made of glass with the refractive index n=1.5 The first side of the lens is plane and the second one is convex spherical with the radius R=30cm . What is the focal length f of the lens? Please select one answer option f=45cm f=60cm f=20cm f=15cm

To find the focal length \( f \) of the lens, we can use the thin lens formula:<br /><br />\[<br />\frac{1}{f} = (n-1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)<br />\]<br /><br />Given:<br />- \( n = 1.5 \)<br />- \( R_1 = \infty \since side is plane)<br />- \( R_2 = 30 \) cm (convex spherical surface)<br /><br />Substituting these values into the formula:<br /><br />\[<br />\frac{1}{f} = (1.5 - 1) \left( \frac{1}{\infty} - \frac{1}{30} \right)<br />\]<br /><br />Since \(\frac{1}{\infty} = 0\):<br /><br />\[<br />\frac{1}{f} = 0.5 \left( -\frac{1}{30} \right)<br />\]<br /><br />\[<br />\frac{1}{f} = -\frac{0.5}{30}<br />\]<br /><br />\[<br />\frac{1}{f} = -\frac{1}{60}<br />\]<br /><br />\[<br />f = -60 \text{ cm}<br />\]<br /><br />Since the focal length is negative, that the focal point is on the same side as the light source, which is typical for a convex lens. Therefore, the correct answer is:<br /><br />\( f = 60 \text{ cm} \)