{"root": {"type": "root", "format": "", "indent": 0, "version": 1, "children": [{"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"mode": "normal", "text": "List-I contains

Question

{"root": {"type": "root", "format": "", "indent": 0, "version": 1, "children": [{"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"mode": "normal", "text": "List-I contains the situation of one or more than one thin lenses (refractive index of the material of each lens is 1.5). The refractive indexes of surrounding media are also given in each case. In List-II contains the information of magnitude of final image distance (in cm) from convex lens in each case.", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}], "direction": null}, {"type": "table", "version": 1, "children": [{"type": "tablerow", "version": 1, "children": [{"type": "tablecell", "version": 1, "headerState": 1, "children": [{"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"mode": "normal", "text": "List - I", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}], "direction": null}]}, {"type": "tablecell", "version": 1, "headerState": 1, "children": [{"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"mode": "normal", "text": "List - II", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}], "direction": null}]}]}, {"type": "tablerow", "version": 1, "children": [{"type": "tablecell", "version": 1, "headerState": 0, "children": [{"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"mode": "normal", "text": "(P) A thin equiconvex lens of focal length 20 cm (in air) is placed so that medium to the left of it is air (", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}, {"type": "math", "inline": true, "version": 1, "equation": "\\mu_{\\text {air }}=1"}, {"mode": "normal", "text": ") and medium to the right of it is water (", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}, {"type": "math", "inline": true, "version": 1, "equation": "\\mu_{\\text {water }}=\\frac{4}{3}"}, {"mode": "normal", "text": "). A point object is placed in air on the principal axis of the lens at a distance 60 cm from it.", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}], "direction": null}, {"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"src": {"src": "https://storage.googleapis.com/mathpix/1789353552_fcc826c9_fig.jpg", "type": "image", "altText": "", "version": 1, "maxWidth": 360}, "type": "image", "altText": "", "version": 1, "maxWidth": 360}], "direction": null}]}, {"type": "tablecell", "version": 1, "headerState": 0, "children": [{"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"mode": "normal", "text": "(1) 240", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}], "direction": null}]}]}, {"type": "tablerow", "version": 1, "children": [{"type": "tablecell", "version": 1, "headerState": 0, "children": [{"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"mode": "normal", "text": "(Q) One of the curved surfaces of a thin equiconvex lens of focal length 60 cm (in air), is silvered. A point object is placed to the left of the lens at a distance 20 cm from the lens.", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}], "direction": null}, {"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"src": {"src": "https://storage.googleapis.com/mathpix/1789353552_14ae81a9_fig.jpg", "type": "image", "altText": "", "version": 1, "maxWidth": 360}, "type": "image", "altText": "", "version": 1, "maxWidth": 360}], "direction": null}]}, {"type": "tablecell", "version": 1, "headerState": 0, "children": [{"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"mode": "normal", "text": "(2) 160", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}], "direction": null}]}]}, {"type": "tablerow", "version": 1, "children": [{"type": "tablecell", "version": 1, "headerState": 0, "children": [{"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"mode": "normal", "text": "(R) Two thin plano-convex lens each of focal length 30 cm (in air) is placed in contact so that their curved surfaces are in contact. Water (", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}, {"type": "math", "inline": true, "version": 1, "equation": "\\mu_{\\text {water }}=\\frac{4}{3}"}, {"mode": "normal", "text": ") is filled in the space between the lenses. The media to the left and right side of the system of the lenses is air (", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}, {"type": "math", "inline": true, "version": 1, "equation": "\\mu_{\\text {air }}=1"}, {"mode": "normal", "text": "). A point object is placed in air at a distance 60 cm from the system as shown.", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}], "direction": null}, {"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"src": {"src": "https://storage.googleapis.com/mathpix/1789353553_7a5b72ac_fig.jpg", "type": "image", "altText": "", "version": 1, "maxWidth": 360}, "type": "image", "altText": "", "version": 1, "maxWidth": 360}], "direction": null}]}, {"type": "tablecell", "version": 1, "headerState": 0, "children": [{"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"mode": "normal", "text": "(3) 180", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}], "direction": null}]}]}, {"type": "tablerow", "version": 1, "children": [{"type": "tablecell", "version": 1, "headerState": 0, "children": [{"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"mode": "normal", "text": "(S) A concave lens of focal length ", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}, {"type": "math", "inline": true, "version": 1, "equation": "\\mathrm{f}_{1}=-20 \\mathrm{~cm}"}, {"mode": "normal", "text": " and an equiconvex thin lens of focal length 40 cm are placed at a distance 28 cm so that their principle axes are coinciding. The surroundings media are shown in the diagram. A point object is placed on the principle axis at a distance 30 cm to the left of concave lens.", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}], "direction": null}, {"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"src": {"src": "https://storage.googleapis.com/mathpix/1789353553_59eb7e45_fig.jpg", "type": "image", "altText": "", "version": 1, "maxWidth": 360}, "type": "image", "altText": "", "version": 1, "maxWidth": 360}], "direction": null}]}, {"type": "tablecell", "version": 1, "headerState": 0, "children": [{"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"mode": "normal", "text": "(4) 80", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}], "direction": null}]}]}, {"type": "tablerow", "version": 1, "children": [{"type": "tablecell", "version": 1, "headerState": 0, "children": [{"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"mode": "normal", "text": "", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}], "direction": null}]}, {"type": "tablecell", "version": 1, "headerState": 0, "children": [{"type": "paragraph", "format": "", "indent": 0, "version": 1, "children": [{"mode": "normal", "text": "(5) 60", "type": "text", "style": "", "detail": 0, "format": 0, "version": 1}], "direction": null}]}]}]}], "direction": null}}

Options:

Answer:

A

Solution:

Lensmaker with surrounding media: apply $\frac{μ _{3}}{v} - \frac{μ _{1}}{u} = \frac{μ _{2} - μ _{1}}{R _{1}} + \frac{μ _{3} - μ _{2}}{R _{2}}$ surface by surface.

(P) Refraction through lens into water gives final image 180 cm from lens. P $\to$ 3

(Q) Silvered back: system acts as mirror of effective power twice the lens; image at 60 cm. Q $\to$ 5

(R) Water lens between two glass lenses: net power gives image at 240 cm. R $\to$ 1

(S) Two-lens separated system traced surface by surface gives 160 cm. S $\to$ 2

Answer: A

TestHub · Accepted Answer