All lay their hands except a deaf-mute, an imbecile, and a minor, since these are not of sound mind. A gentile likewise: the children of Israel lay their hands, but the nations do not lay their hands. But the blind person, what is the reason he does not lay his hands? Rav Chisda and Rav Yitzchak bar Avdimi differed. One said: laying on of hands is derived from the elders of the congregation. The other said: it is derived from the burnt offering brought for the festival appearance. According to the one who derives it from the festival appearance offering, why does he not learn it from the elders of the congregation? Because we derive an individual's case from an individual's case and do not derive an individual's case from a communal case. And according to the one who learns it from the elders of the congregation, why does he not learn it from the festival appearance offering? Because we derive a matter in which laying on of hands is written in its own context from a matter in which laying on of hands is written in its own context, thereby excluding the festival appearance offering, which itself is learned from the freewill burnt offering. A reciter recited before Rav Yitzchak bar Avdimi: "And he brought the burnt offering and performed it according to the rule" (Leviticus) means according to the rule of the freewill burnt offering, teaching about the obligatory burnt offering that it requires laying on of hands. "A man": to include the converts. "Of you": to exclude the apostates. And what did you see to reason thus? Say rather "of you" to include apostates and "a man" to exclude converts! After Scripture both broadened and narrowed, Scripture says "the children of Israel": just as the children of Israel are those who accepted the covenant, so converts are those who accept the covenant; this excludes apostates, who do not accept the covenant. If so, just as the children of Israel are the children of those who accepted the covenant, so apostates are the children of those who accepted the covenant; this would exclude converts, who are not the children of those who accepted the covenant. Therefore Scripture says "of you." And now do not say otherwise than: just as Israel accepted the covenant, so converts accept the covenant; this excludes apostates, who do not accept the covenant.
All May Lay Hands on the Offering and the Convert Who Keeps the Covenant
Yalkut Shimoni on Torah 434:4
הַכֹּל סוֹמְכִין חוּץ מֵחֵרֵשׁ שׁוֹטֶה וְקָטָן דְּלָאו בְּנֵי דֵּעָה נִינְהוּ, נָכְרִי נַמִּי בְּנֵי יִשְׂרָאֵל סוֹמְכִין וְאֵין הַגּוֹיִים סוֹמְכִין. אֶלָּא סוּמָא מַאי טַעְמָא לֹא, רַב חִסְדָּא וְרַב יִצְחָק בַּר אַבְדִּימִי חָד אָמַר, אָתְיָא סְמִיכָה מִזִּקְנֵי הָעֵדָה, וְחָד אָמַר אָתְיָא סְמִיכָה מֵעוֹלַת רְאִיָּה, וּלְמָאן דְּאָמַר מֵעוֹלַת רְאִיָּה מַאי טַעְמָא לֹא יָלִיף מִזִּקְנֵי הָעֵדָה, דָּנִין יָחִיד מִיָּחִיד וְאֵין דָּנִין יָחִיד מִצִּבּוּר וּלְמָאן דְּיָלִיף מִזִּקְנֵי הָעֵדָה מַאי טַעְמָא לֹא יָלִיף מֵעוֹלַת רְאִיָּה, דָּנִין מִידִי דִּכְתִיב בֵּיהּ סְמִיכָה בְּגוּפֵיהּ מִמִּידִי דִּכְתִיב בֵּיה סְמִיכָה בְּגוּפֵיהּ, לְאַפּוּקֵי עוֹלַת רְאִיָּה דְּהִיא גּוּפָהּ מֵעוֹלַת נְדָבָה גְּמִיר. תָּנֵי תַּנָּא קָמֵיהּ דְּרַב יִצְחָק בַּר אַבְדִּימִי "וַיַּקְרֵב אֶת הָעֹלָה וַיַּעֲשֶׂהָ כַּמִּשְׁפָּט", כְּמִשְׁפַּט עוֹלַת נְדָבָה, לִמֵּד עַל עוֹלַת חוֹבָה שֶׁטְּעוּנָה סְמִיכָה. אָדָם, לְרַבּוֹת אֶת הַגֵּרִים מִכֶּם לְהוֹצִיא אֶת הַמּוּמָרִין, וּמַה רָאִיתָ, אֵימָא מִכֶּם לְרַבּוֹת מוּמָרִים אָדָם לְהוֹצִיא גֵּרִים, אַחַר שֶׁרִבָּה הַכָּתוּב וּמִעֵט תַּלְמוּד לוֹמַר "בְּנֵי יִשְׂרָאֵל" מַה בְּנֵי יִשְׂרָאֵל מְקַבְּלֵי בְּרִית, אַף גֵּרִים מְקַבְּלֵי בְּרִית, יָצְאוּ מוּמָרִים שֶׁאֵינָן מְקַבְּלֵי בְּרִית. אִי מַה בְּנֵי יִשְׂרָאֵל בְּנֵי מְקַבְּלֵי בְּרִית, אַף מוּמָרִים בְּנֵי מְקַבְּלֵי בְּרִית, יָצְאוּ גֵּרִים שֶׁאֵינָן בְּנֵי מְקַבְּלֵי בְּרִית, תַּלְמוּד לוֹמַר "מִכֶּם" וְעַכְשָׁו אַל תֹּאמַר אֶלָּא מַה יִשְׂרָאֵל מְקַבְּלֵי בְּרִית אַף הַגֵּרִים מְקַבְּלֵי בְּרִית, יָצְאוּ מוּמָרִים שֶׁאֵינָן מְקַבְּלֵי בְּרִית.